Correlations and Coherence at Different Scales (CCDS25)

In this talk, I will discuss the difference between a classical reservoir (which adds no additional quantum degrees of freedom) and a quantum reservoir (which does add quantum degrees of freedom). I will then explain why the classical reservoir is preferred for pure-state creation, because it cannot create mixed states. Then I will describe an efficient algorithm for ground-state preparation of the Hubbard model that avoids the need for Jordan-Wigner strings in the ansatz and just employs hopping terms and on-site correlations in preparing the ground state. I believe this is perhaps the most efficient way to create ground states. I will also show how this approach compares to other methods for ground-state preparation such as couple-cluster approaches. I may even have some preliminary results for how well this methodology works in quantum chemistry ground-state preparation. The approach does require a global optimization strategy, which is complicated to implement, but this is ameliorated by the fact that the number of parameters can be kept rather small (empirically appearing to grow linearly with the number of sites/orbitals in the system). Our results have recently appeared in Phys. Rev. B 111, 235152 (20025).

This work was completed in collaboration with Zach He, Lex Kemper, Lorenzo Del Re, and Dominika Zgid.

The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge, at the forefront of condensed matter physics and computational chemistry alike, and it is one of the targets for quantum computing. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some correlated behavior, but it is limited by the need to calculate the Green’s function for the impurity model. We propose a framework for DMFT calculations on quantum computers, focusing on near-term applications.
It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins the Gaussian state preparation with the time evolution to compute the necessary Green's functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of the circuit compression by extracting the impurity Green's function on IBM quantum processors for a single impurity coupled to three bath orbitals
(8 physical qubits and 1 ancilla). We discuss the potential paths forward towards realizing this use case of quantum computing in materials science.

Analytic continuation is a central step in the simulation of finite-temperature field theories in which numerically obtained imaginary-time data is continued to the real frequency axis for physical interpretation. Numerical analytic continuation is considered to be an ill-posed problem where uncertainties on the Matsubara axis are amplified exponentially. This talk introduces new class of algorithms, based on the mathematical framework of Nevanlinna theory combined with numerical methods from signal processing and control theory, which overcome the ill-posed nature of the problem and offer systematically improvable continuations, thereby facilitating the interpretation of computational results from finite-temperature field theories.

Understanding transport in interacting quantum many-body systems is a central challenge in condensed matter and statistical physics. Numerical studies typically rely on two main approaches: Dynamics of linear-response functions in closed systems and Markovian dynamics governed by master equations for boundary-driven open systems. While the equivalence of their dynamical behavior has been explored in recent studies [1], a systematic comparison of the transport coefficients obtained from these two classes of methods remains an open question. Here [2], we address this gap by comparing and contrasting the dc diffusion constant $\mathcal{D}_{\text{dc}}$ computed from the aforementioned two approaches. We find a clear mismatch between the two, with $\mathcal{D}_{\text{dc}}$ exhibiting a strong dependence on the system-bath coupling for the boundary-driven technique, highlighting fundamental limitations of such a method in calculating the transport coefficients related to the asymptotic dynamical behavior of the system. We trace the origin of this mismatch to the incorrect order of limits of time $t \rightarrow \infty$ and system size $L\rightarrow \infty$, which we argue to be intrinsic to boundary-driven setups. As a practical resolution, we advocate computing only time-dependent transport coefficients within the boundary-driven framework, which show excellent agreement with those obtained from the Kubo formalism based on closed-system dynamics, up to a time scale set by the system size. This leads us to interpret the sensitivity of the dc diffusion constant on the system-bath coupling strength in an open system as a potential diagnostic for finite-size effects.

[1] T. Heitmann, J. Richter, F. Jin, S. Nandy, Z. Lenarčič, J. Herbrych, K. Michielsen, H. De Raedt, J. Gemmer, R. Steinigeweg, Phys. Rev. B 108, L201119 (2023).
[2] M. Kempa, M. Kraft, S. Nandy, J. Herbrych, J. Wang, J. Gemmer, R. Steinigeweg, arXiv:2507.16528.

Iconic features of classical dissipative dynamics include persistent
limit-cycle oscillations and critical slowing down at the onset of such
oscillations, whereby the system relaxes purely algebraically in time. On the other hand, quantum systems subject to generic Markovian dissipation decohere exponentially in time, approaching a unique steady state. We show how coherent limit-cycle oscillations and algebraic decay can emerge in a quantum system governed by a Markovian master equation. We illustrate these mechanisms using a single-spin model motivated by Landau-Lifshitz-Gilbert dynamics.

The interplay of disorder, electronic correlations, and superconducting fluctuations in vanadium-titanium and niobium-titanium alloys is investigated using the coherent potential approximation (CPA) and dynamical mean-field theory (DMFT). For V-Ti alloys [1], the superconducting transition temperature $T_c$, estimated with the McMillan formula, shows a maximum at a Ti concentration near 0.33 for $U$ between 2 and 3 eV, in agreement with the experimentally observed $T_c$ increase of about 20%. For niobium and Nb$_{0.44}$Ti$_{0.56}$ in the bcc phase up to 250 GPa [2], significant topological changes in the Fermi surface and a weakening of correlations are found with increasing pressure. The normal state remains a Fermi liquid with well-defined quasiparticles. These results provide insight into the electronic states near the Fermi level relevant for the robust superconductivity of Ti-doped niobium under compression and highlight the need for further experimental studies. A connection is established between disorder-induced modifications of the electronic structure and superconducting properties, offering a framework for understanding robust superconductivity under varying disorder and pressure conditions.

[1] D. Jones, A. Östlin, A. Weh, F. Beiuseanu, U. Eckern, L. Vitos, L. Chioncel, Phys. Rev. B 109, 165107 (2024)
[2] D. Jones, A. Östlin, A. Chmeruk, F. Beiuseanu, U. Eckern, L. Vitos, L. Chioncel, Phys. Rev. B 111, 165152 (2025)

Massless Dirac fermions in one-dimensional systems provide a fertile ground for exploring non-Fermi liquid behavior and interaction-driven topological phases. However, the numerical simulation of such systems has long been hindered by the fermion doubling problem, which introduces spurious low-energy modes in standard lattice discretizations. In our work [1], we present a novel approach that circumvents this obstruction by discretizing both space and time through a local Lagrangian formulation of a helical Luttinger liquid with Hubbard interaction.

Our method employs a tangent fermion dispersion, which preserves the single Dirac cone and its topological protection while remaining free from fermion doublers. Whithin this framework we perform sign-free quantum Monte Carlo simulations, enabling direct comparison with bosonization predictions. The observed power-law decay of correlation functions confirms the fidelity of the approach and its consistency with the continuum limit.

Beyond enabling simulations of strongly interacting Dirac fermions, our results clarify the crucial role of dispersion choice: as shown in our complementary tensor network study [2], a tangent dispersion reproduces correct critical behavior, while conventional sine discretization fails. Taken together, these insights lay the groundwork for reliable lattice simulations of interacting Dirac matter.

[1] Helical Luttinger liquid on a space-time lattice.
V. A. Zakharov, J. Tworzydlo, C. W. J. Beenakker, M. J. Pacholski
Phys. Rev. Lett. 133, 116501 (2024).
[2] Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions.
V. A. Zakharov, S. Polla, A. Donís Vela, P. Emonts, M. J. Pacholski, J. Tworzydlo, C. W. J. Beenakker
Phys. Rev. Research 6, 043059 (2024).

Recent experiments on bosonic atoms, confined in 2D optical lattices and exposed to a leaky optical cavity, have revealed intriguing self-organization phenomena, including the coexistence of phase coherence and charge order characteristic of supersolid phases.
Mean field theories of such systems typically rely on the cavity adiabatic elimination, yielding an effective Bose-Hubbard model with infinite-range interactions. This approximation misses important effects, related to the dissipative nature of the cavity, that we unveiled by performing truncated Wigner simulations of the full quantum dynamics for large 2D lattices [1]. We show that the relaxation of the system towards the steady state is quite slow compared to the timescales of the bosons and phase coherence displays quasi-long range order. Based on an accurate finite-size scaling analysis, we show that in the strong coupling regime the cavity induces a Berezinskii-Kosterlitz-Thouless phase transition, where the supersolid turns into a charge density wave insulator.

[1] G. Orso, J. Zakrzewski and P. Deuar, Self-organized cavity bosons beyond the adiabatic elimination approximation, Physical Review Letters 134, 183405 (2025).

Extracting information from quantum many-body systems remains a key challenge in quantum technologies due to experimental limitations. In this work [1], we employ a single spin qubit to probe a strongly interacting system, creating an environment conducive to qubit decoherence. By focusing on the XXZ spin chain, we observe diverse dynamics in the qubit evolution, reflecting different parameters of the chain. This demonstrates that a spin qubit can probe both quantitative properties of the spin chain and qualitative characteristics, such as the bipartite entanglement entropy, phase transitions, and perturbation propagation velocity within the system. This approach reveals the power of small quantum systems to probe the properties of large, strongly correlated quantum systems.

[1] M. Płodzień, S. Das, M. Lewenstein, C. Psaroudaki, and K. Roszak, Phys. Rev. B 111, L161115 (2025)

We unveil signatures of multipolar current phases in layered perovskite Sr2RuO4 and kagome CsTi3Bi5 [1,2]. This is done using circularly polarized, spin-selective, angular-resolved photoelectron spectroscopy, which shows intriguing asymmetry between spin-up and spin-down signals. In both cases a multipolar, spin-orbital current phases are postulated to account for this effect as more conventional types of order must be excluded as incoherent with experiments. In both cases we develop description of the spin-dichroic signal by means of a tight-binding model with a special form of a time-reversal symmetry.

[1] F. Mazzola, W. Brzezicki,..., M. Cuoco, Anomalous spin-optical helical effect in Ti-based kagome metal, arXiv:2502.19589.
[2] F. Mazzola, W. Brzezicki,..., A. Vecchione, Signatures of a surface spin–orbital chiral metal , Nature 626, 752 (2024).

The interaction between a strong laser field and matter results in a non-linear optical process that gives rise to the generation of high harmonics of the incident frequency, which has emerged as a transformative technique for studying electronic systems, a contribution recognized with the 2023 Nobel Prize in Physics.

Recently, there has been a growing interest in the use of high harmonic generation (HHG) to probe various properties of matter, as it can track the electronic motion at the attosecond time scales in both gases and solid state systems. Spectroscopy based on the HHG can serve as a tool of ultrafast imaging to detect signatures of quantum phase transitions in high-temperature superconductors, distinguish between trivial and nontrivial topological phases, and probe dynamical and structural properties of electrons.

Here, we present theoretical results for high-harmonic spectroscopy as a method of phase detection in a strongly correlated system modeled by the extended Hubbard Hamiltonian. Moreover, we show that the temporal behaviour of a laser-driven electron dynamics reveals information about low-energy excitations and allows tracking the system through cluster formation accompanying the first-order phase transition.

The Dicke model is a central platform for exploring strong light-matter interaction and its superradiant properties, with implications for emerging quantum technologies. Recognizing that realistic qubits inherently experience direct interactions, we investigate the influence of both isotropic and anisotropic spin-spin couplings on the Dicke paradigm. In the strong coupling regime--where large photon populations challenge conventional numerical techniques--we developed a hybrid numerical method tailored for this problem, which demonstrates high accuracy and rapid convergence in reproducing established Dicke model results. Furthermore, our study reveals that distinct ferromagnetic and antiferromagnetic regions exhibit different orders of phase transitions. Most notably, in the presence of anisotropic interactions, we identify a novel phase where spin order and superradiance coexist, marked by enhanced superradiance with a photon number significantly exceeding that of the conventional Dicke model.

The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), including cluster-DMFT, one usually obtains the Green's function in imaginary-time. The process of inverting a Laplace transform to obtain the spectral function in real-frequency is an ill-posed problem and forms the core of the analytic continuation problem. We propose to use a completely unsupervised autoencoder-type neural network to solve the analytic continuation problem. We introduce an encoder-decoder approach that, together with only minor physical assumptions, can extract a high-quality frequency response from the imaginary time domain. With a deeply tunable architecture, this method can, in principle, locate sharp features of spectral functions that might normally be lost using already well-established methods, such as maximum entropy (MaxEnt) methods. We demonstrate the strength of the autoencoder approach by applying it to QMC results of imaginary time Green's functions for a single-band Hubbard model. The proposed method is general and can also be applied to other ill-posed inverse problems.

Recently, a new form of magnetism, called altermagnetism, has been discovered, beyond the previously well-established ferro- and antiferromagnetism possibilities. Altermagnets break spin-degeneracy, as in a ferromagnet, but with a momentum dependent spin splitting resulting in zero net magnetization, as in antiferromagnets. Due to their unique magnetization, altermagnets also produce intriguing possibilities for other ordered phases of matter. Magnetism and superconductivity are two of the most celebrated quantum phases of matter and usually have a ‘friend-foe’ dichotomous relation, but combining superconductivity with altermagnetism turns out to open for new exceptional possibilities. In this talk I will show several novel effects occurring when superconductivity appears in an altermagnet, including finite momentum pairing, field-induced superconductivity, and a perfect superconducting diode effect, as well as demonstrate constraints on the possible superconducting pairing.

We use density matrix renormalization group (DMRG) and variational exact diagonalization (VED) to calculate the single-electron removal spectral weight for the Hubbard-Holstein model at low electron densities. Tuning the strength of the electron-phonon coupling and of the Hubbard repulsion allows us to contrast the results for a liquid of polarons versus a liquid of bipolarons. The former shows spectral weight up to the Fermi energy, as expected for a (uncorrelated) metal. The latter has a gap in its spectral weight, set by the bipolaron binding energy, although this is also a (strongly correlated) metal. This difference suggests that angle-resolved photoemission spectroscopy could be used to identify liquids of pre-formed pairs. Furthermore, we show that the liquid of bipolarons is well approximated by an ensemble of bosons that are hard-core in momentum space, filling the states inside the Fermi sea but otherwise non-interacting [1].

In the second part I will discuss the two-electron removal spectral weight for the Hubbard-Holstein model, starting from the ground-state with two electrons on a one-dimensional chain. We argue that this spectral weight provides a valuable proxy for the intensity of 2e-ARPES processes. Our results show that when contrasted to the (large) signal due to two electrons ejected from two different pairs, the (much
weaker) signal due to two electrons ejected from the same pair (i) is segregated in energy, appearing at a lower binding energy, and (ii) has a very characteristic momentum dependence, with different symmetry than that corresponding to two electrons emitted from two different pairs [2].

[1] K. Kovac, A. Nocera, A. Damascelli, J. Bonca, and M. Berciu, Phys, Rev. Lett. 134, 096502 (2025)
[2] J. Bonca, A. Damascelli, and M. Berciu, in preparation

Stripe order and its intricate relationship with high-temperature superconductivity remain central puzzles in strongly correlated electron systems. In this talk, I synthesize recent theoretical advances illuminating this relationship on the basis of two complementary studies. The first, leveraging modern tensor network simulations, demonstrates that in the two-dimensional Fermi Hubbard model, enhanced charge susceptibility near 1/8 hole doping arises from transient clustering of charge carriers—pointing to a precursor state where phase separation is forestalled by the eventual emergence of stripe order. The second study dives into the superconducting ground state within stripe-ordered phases, revealing via density matrix renormalization group methods that Cooper pair condensation is inherently fragmented: multiple macroscopically occupied condensates localize along the stripes and hybridize into a collective quantum state across the system. Together, these results highlight how fluctuations between charge clustering, stripe order, and unconventional superconductivity give rise to the rich phase behavior in cuprate-like models. This new perspective advances our understanding of the origin of the strange metal and pseudogap regimes, and offers fresh insights into the nature of pairing and long-range order in strongly correlated materials.

Understanding the material constraints that limit the critical temperature (Tc) is therefore pertinent to applied materials research, as well as our fundamental understanding of this remarkable phase of matter. In many strongly correlated materials, where estimating Tc is notoriously hard, we can place stringent constraints on the maximum possible Tc. I will present rigorous upper bounds on Tc in terms of the optical conductivity sum-rule, which is easier to measure experimentally and estimate theoretically. These constraints follow from exact upper bounds on the superfluid stiffness, an experimental measure of the rigidity of the U(1) phase that defines a superconductor. I will demonstrate the utility of these bounds for three strongly correlated materials of current interest. In a broad class of materials with flat bands, the low frequency optical conductivity may be dominated by a quantum geometric contribution - an inherently multi-band effect of non-trivial rotations in the Hilbert space of Bloch eigenfunctions in response to a vector potential. For these systems, I will present tighter bounds on the stiffness and 2D Tc in terms of the minimal spatial extent of the flat band eigenfunctions – demonstrating a deep connection between low energy optical conductivity and the Hilbert space geometry of multi-band Bloch Hamiltonians. Appreciating the limits on Tc in the presence of strong correlations helps us not only to benchmark materials in terms of their potential for higher Tc but also leads to qualitative insights guiding the search for strongly correlated materials where the maximum Tc is higher.

We discuss role of the correlation effects due to the Coulomb repulsion between electrons of quantum impurities placed on interface of superconductors, focusing on their interplay with the proximity effect. We show how these competing phenomena can be observed under nonequilibrium conditions imposed e.g. by external magnetic fields, gate potentials, periodic driving, etc. Specific examples will be given, both for the conventional and the topologically nontrivial superconducting nanostructures.

I discuss the thermalization of closed quantum systems. This refers to their ability to relax toward steady states described by only a few quantities, such as mean energy or particle number. I introduce the eigenstate thermalization hypothesis, which underpins our current understanding of this process. I then present notable exceptions to thermalization, focusing on Hilbert space fragmentation, where the Hamiltonian breaks into exponentially many (in system size) dynamically disconnected blocks. In the final part, I show that a suitably chosen perturbation can induce a gradual merging of these fragmented subspaces. This slow restoration of ergodicity gives rise to an extended critical regime, marked by multiple peaks in the fidelity susceptibility. Each peak signals a change in the number of blocks and corresponds to ultra-slow relaxation of local observables.

We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$.

Quantum integrable systems are characterized by an infinite number of conserved charges and stable quasi-particle excitations. When integrability is broken, interactions between quasi-particles are introduced, opening the way for a novel kinetic theory that incorporates both integrable and non-integrable processes. In this talk I will review recent advances in the development of such a kinetic framework, which provides new insights into a range of non-equilibrium phenomena. These include the thermalization of homogeneous systems, the emergence of the Navier-Stokes equations, and the generalization of the famous BBGKY hierarchy.

The random matrix theory (RMT) has been a hallmark in the study of quantum thermalization as it sets a link between properties of random matrix eigenstates and observable matrix elements. Nevertheless, this description is incomplete for lattice models. A more relevant picture is given by the eigenstate thermalization hypothesis (ETH), which takes into account the local structure of the Hamiltonian and introduces an energy scale, dubbed Thouless energy, separating universal RMT dynamics from local Hamiltonian dynamics. Recently, this picture has been extended to systems in the vicinity of an ergodicity breaking phase transition, where the Thouless energy becomes vanishingly small. This phenomenon, denoted fading ergodicity [\href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.134206}{Phys. Rev. B 110, 134206}], shows how fluctuations of matrix elements soften whence an eigenstate transition is approached. Here, following the approach in the seminal work by Deutsch we show that within RMT one can derive the softening of matrix elements fluctuations from the properties of eigenstate coefficients. Remarkably, there exist a direct relation to the fractal nature of its eigenstates in the unperturbed basis. We then extend our analysis to the Ultrametric matrix and Rosenzweig-Porter matrix ensembles. We argue that these RMT models, share some remarkably similar dynamical properties of physical observables before the onset of localization. Our results reveal that the fading ergodicity gives rise to universal features of anomalously slow dynamics and unveil a potentially accessible measure, the noise spectrum, as a probe of emergent nonthermal behaviour.

One of the main paradigms of quantum magnetism is that collective excitations in systems with long-range order, such as ferro- or antiferro-magnets, are well described in terms of bosonic quasiparticles -- magnons. This approach has been extremely successful, largely because magnons interact only weakly.

However, when long-range order collapses -- for example, due to geometric frustration or doping-induced disruption of spin couplings -- magnons begin to interact strongly, and this description breaks down. In such cases, the low-energy magnetic excitations are typically described in terms of spinons. Unfortunately, spinons are less intuitive, as they carry fractional quantum numbers and obey fractional statistics.

In this talk, I will first explain our recent efforts to develop an intuitive understanding of both the magnon [1] and the spinon [2], thereby highlighting the intrinsic differences between these two quasiparticles. In the second part of the talk, I will briefly discuss the extent to which a spinon- or magnon-based approach better explains some of the most well-known experimental magnetic spectra of high-Tc​ cuprates [3].

[1] P. Wrzosek et al.; Phys. Rev. B 102, 02440 (2020).
[2] T. Kulka et al., Phys. Rev. Lett. 134, 236504 (2025).
[3] Y.F. Kung et al., Phys. Rev. B 96, 195106 (2017); E.M. Paerschke et al., Phys. Rev. B 99, 205102 (2019); W. Zhang et al., npj Quantum Mater. 7, 123 (2022).

We examine the onset of Anderson localization in three-dimensional systems with structural disorder in form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of lattice regularities, we show that the Anderson localization transition occurs when the strength of the structural disorder is smoothly increased. Performing finite-size scaling analysis, we show that the transition belongs to the same universality class as regular Anderson localization induced by on-site disorder. Our paper identifies a class of structurally disordered lattice models in which destructive interference of matter waves may inhibit transport and lead to a transition between metallic and localized phases.

Local integrals of motion (LIOMs) play a key role in understanding the stationary states of closed macroscopic systems. They were found for selected integrable systems via complex analytical calculations. The existence of LIOMs and their structure can also be studied via numerical methods, which, however, involve exact diagonalization of Hamiltonians, posing a bottleneck for such studies. We show that finding LIOMs in translationally invariant lattice models or unitary quantum circuits can be reduced to a problem for which one may numerically find an exact solution also in the thermodynamic limit. We develop and implement a simple algorithm and demonstrate the efficiency of this method by calculating LIOMs and the Mazur bounds for infinite integrable spin chains and unitary circuits. Finally, we demonstrate that this approach correctly identifies approximate LIOMs in nearly integrable spin ladders and estimates the relaxation times.

We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on the Fock-space graph in the particle occupation basis, which encodes configurations connected by a given Hamiltonian. To quantify hierarchical structures, we develop a measure of centrality of the nodes, which is applicable to generic Hamiltonian matrices and inspired by established centrality measures from graph theory. We illustrate these ideas in the quantum East (QE) model. We introduce several ways of detuning nodes in the corresponding graph that alter the hierarchical structure, defining a family of QE models. We numerically demonstrate how these detunings affect the degree of non-ergodicity on finite systems, as evidenced by both the time dependence of density autocorrelations and eigenstate properties in the detuned QE models.

Recent experiments on novel materials, which are well represented by $S=1/2$ easy-axis spin models on triangular lattice, stimulated renewed theoretical interest in basic properties of anisotropic spin models on frustrated planar lattices. While the thermodynamic properties of the model on the kagome lattices reveal the spin-liquid scenario in the whole range of anisotropies, the case of the triangular lattice is more complex. Spin-wave theory and several numerical studies indicate that
the anisotropic systems should follow the supersolid scenario with ground-state broken translational symmetry and as well the transverse magnetic order, implying the gapless Goldstone mode. Confirming this scenario at finite magnetic fields, we find numerically at zero field the evidence for a solid with a finite gap, reflected in several quantitites. The origin can be traced back to the effects of strong correlations, manifested also in simpler reduced models.

We report disorder-free localization of Majorana fermions on intermediate time scales in an emergent gapless non-integrable $Z_2$ quantum spin liquid. A large density of ground-state visons induced by an external magnetic field provides coherent flux disorder that (i) closes the Majorana fermion gap and (ii) localizes the fermions while preserving translation symmetry. The resulting Majorana metallic state is confirmed by the close agreement between the numerically obtained dynamical spin spectral function and the Majorana spectral function of an effective tight-binding model with coherent vison disorder. Compelling evidence of its localization is provided by the time evolution of the local energy density, which shows negligible spreading after a local quench on its ground state; and a vanishing energy current response despite the gapless energy spectrum. These results demonstrate that the disorder-free localization can also occur near equilibrium at low energy, and offer an explanation to the thermal paradox in recent experiments where a linear specific heat coexists with vanishing thermal transport in frustrated Mott insulators with neutral Fermi surfaces.

Hidden phases, which cannot be reached via a thermal pathway, are a conceptually interesting and technologically relevant subject of nonequilibrium condensed matter studies. Strongly correlated electron systems with spin, charge, and orbital degrees of freedom exhibit competing ordering tendencies, and thus provide a rich platform for the search of nonthermal phases. Recent advances in the theoretical description of strongly-correlated nonequilibrium systems, in particular the development of nonequilibrium dynamical mean field theory, have enabled systematic explorations of such hidden states. In this talk, I will present several examples of nonthermal electronic orders in photo-excited correlated lattice systems. This includes nonthermal spin, orbital and charge order [1,2,3], nonthermal excitonic order [4,5], nonthermal composite order [6], and nonthermal superconducting states [7-10].

[1] J. Li, H. Strand, P. Werner, and M. Eckstein, Nat. Comm. 9, 4581 (2018).
[2] S. Ray and P. Werner, Phys. Rev. B 110, 214433 (2024) (2024).
[3] Y. Murakami, S. Takayoshi, T. Kaneko, A. M. Laeuchli and P. Werner, Phys. Rev. Lett. 130, 106501 (2023).
[4] P. Werner and Y. Murakami, Phys. Rev. B 102, 241103 (2020).
[5] S. Ray and P. Werner, in preparation (2025).
[6] P. Werner and Y. Murakami, Phys. Rev. B 104, L201101 (2021).
[7] J. Li, D. Golez, P. Werner and M. Eckstein, Phys. Rev. B 102, 165136 (2020).
[8] J. Li, M. Mueller, A. Kim, A. Laeuchli, and P. Werner, Phys. Rev. B 107, 205115 (2023).
[9] S. Ray, Y. Murakami, and P. Werner, Phys. Rev. B 108, 174515 (2023).
[10] S. Ray and P. Werner, Phys. Rev. B 110, L041109 (2024).

In 1965 Kohn and Luttinger proposed a genuine electronic mechanism for superconductivity. Despite the bare electrostatic interaction between two electrons being repulsive, in a metal electron-hole fluctuations can give rise to Friedel oscillations of the screened Coulomb potential. Cooper pairing among the electrons then emerges when taking advantage of the attractive regions. Focusing on monolayer NbSe$_2$ and TaS$_2$, two intrinsic Ising superconductors, we devloped a bottom-up multi-orbital approach to evaluate the screened interaction microscopically. In the direct space, we find long-range Friedel oscillations alternating in sign, a key to the Kohn-Luttinger mechanism. The momentum-resolved gap equations predict for both systems a chiral gap with $p$-like symmetry. However, the different momentum dependence results in seemingly different tunneling spectra, with a hard gap for NbSe$_2$ and a V-like shape for TaS$_2$, respectively. Our predictions are in agreement with recent tunneling spectroscopy measurements.

We take literally the Hubbard model with the identical form of interaction, as in the original model, but the Hubbard parameter U describes the repulsive interaction in the k-space. This form allows in a simple manner to analyze the properties of the model in an exact manner for arbitrary value of U. Explicitly, we analyze the situation with
$U \to \infty$. We consider this model in the situation with spin-dependent effective masses of such quasiparticles and discuss in detail the evolution of indistinguishable system of quantum particles into their distinguishable correspondence and back. At the end, a possibility of observing such a transmutation of particle statistics is stressed.

Project partially supported by NCN Grant Nos. UMO–2021/41/B/ST3/04070 and UMO–2023/49/B/ST3/03545.

We present a versatile framework for constructing effective models of superconducting (SC) heterostructures described by the generalized SC Anderson Impurity Model (SC-AIM) with multiple impurities and leads. Our method, Chain Expansion (ChE), maps superconducting leads onto finite one-dimensional chains, enabling efficient simulations while retaining essential physical properties. The mapping can be tailored to optimally capture either low-energy physics or the full-bandwidth tunneling self-energy.

We derive simple analytical expressions to generate chains suited for different computational tasks, including ground state analysis and real-time evolution. Benchmarking against Numerical Renormalization Group (NRG) results, we demonstrate that ChE-based models exhibit excellent agreement with full SC-AIM solutions across a broad parameter space—even when using short chains amenable to Exact Diagonalization (ED). Accuracy systematically improves with chain length, and longer chains remain tractable due to the method’s one-dimensional structure, which is compatible with Density Matrix Renormalization Group (DMRG) techniques. Time dynamics computed using ChE align well with non-equilibrium Green’s function approaches.

After validating ChE on benchmark systems, we explore complex setups involving multiple quantum dots in serial and parallel configurations. We analyze their tunability, intricate phase diagrams, and the role of parity in shaping Andreev bound states (ABS) and supercurrent behavior.

Machine learning (ML) methods have shown great potential in tackling challenging problems within condensed matter physics and quantum many-body systems. In this talk, I will present recent developments from our research on leveraging deep learning (DL) techniques to reconstruct the effective Hamiltonian of quantum dot (QD) arrays from transport measurements, particularly focusing on conductance maps as a function of gate voltages.

QDs defined by electrostatic gating, which host individual electrons or holes, are promising candidates for scalable quantum computing and quantum simulator platforms. A particularly compelling application involves simulating minimal Kitaev chain models [1], which host so-called poor man's Majorana modes [2]. Accurately identifying (or autotuning) the Hamiltonian parameters of these systems from experimental data remains a significant challenge [4-5].

Our proposed approach employs a physics-informed autoencoder architecture consisting of a deep residual convolutional neural network (e.g. ResNet) or Vision Transformer encoder to predict the QD Hamiltonian parameters. The decoder is a differentiable module (implemented in PyTorch) employing an analytical Green’s function formalism to calculate conductance from these predicted parameters. The entire system is trained end-to-end, optimizing the reconstruction of the input conductance maps.

Embedding physical principles directly within the neural network (NN), using technique we previously developed [6], facilitates physically meaningful predictions and efficient generalization. The method represents a step forward in geometric DL, explicitly integrating physical constraints into the NN architecture, and provides a powerful framework for experimentally relevant Hamiltonian reconstruction in quantum simulation platforms.

[1] M. Leijnse and K. Flensberg, Phys. Rev. B 86, 134528 (2012).
[2] G. Dvir et al., Nature 614, 445 (2023).
[3] D. Koch et al., Phys. Rev. Appl. 20, 044081 (2023).
[4] J. Wang et al., Nature Physics 13, 551 (2017).
[5] V. Gebhart et al., Nature Reviews Physics 5, 141 (2023).
[6] M. Krawczyk et al., Phys. Rev. A 109, 022405 (2024).

We systematically investigate the phase diagram of a parallel double-quantum-dot Andreev molecule, where the two quantum dots are coupled to a common superconducting lead. Using the numerical renormalization group method, we map out the evolution of the ground state across a wide parameter space of level detunings, size of the superconducting gap, lead couplings, and interdot coupling strength. The intricate phase diagrams feature singlet, doublet, and a relatively uncommon triplet ground states, with the latter being a distinct signature of strong lead-mediated interactions between the quantum dots.
We benchmark the applicability of simplified effective models, including the atomic limit and zero-bandwidth approximations, in capturing the complex behavior of this parallel configuration. Our analysis reveals severe limitations of these models, underscoring the necessity for maximal caution when extrapolating beyond their tested validity. In particular, all effective models except for the extended version of the zero-bandwidth approximation failed in reproducing the triplet ground state and made several false predictions [1].
We qualitatively as well as quantitatively recover the NRG results for half-filled dots by straightforward, yet quite tedious 4th order perturbative calculation in the dot-SC-lead tunnel coupling. The analysis of the analytical approach reveals the microscopic mechanism behind the numerical findings as well as the causes of the failure of the simplified effective models [2].
These findings provide crucial insights for interpreting experimental observations and designing superconducting devices based on quantum-dot architectures.

Acknowledgements
This work was supported by Grant No. 23-05263K of the Czech Science Foundation and the National Science Centre (Poland) through the Grant No. 2022/04/Y/ST3/00061.

[1] Peter Zalom, Kacper Wrześniewski, Tomáš Novotný, and Ireneusz Weymann, “Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models”, Phys. Rev. B 110, 134506 (2024) doi: 10.1103/PhysRevB.110.134506
[2] Sachin Verma, Peter Zalom, and Tomáš Novotný, “Singlet-triplet quantum phase transition in a half-filled double quantum dot Andreev molecule”, in preparation (2025)

In this work, we present a refrigeration device based on the cooling by heating principle, where a quantum dot mediates energy transfer between two ferromagnetic metals and a hot magnetic insulator. Magnons from the magnetic insulator drive hot electrons from the colder to the hotter ferromagnetic electrode, resulting in cooling of the cold metallic lead. Our calculations reveal that the coefficient of performance depends on the quantum dot energy level, magnetic field, and electrode polarization. Optimal cooling is achieved with fully spin-polarized electrodes in an antiparallel magnetic configuration. However, as spin polarization decreases, a significant parasitic heat flow arises due to unwanted spin-down electrons entering the cold reservoir. This parasitic current not only reduces the net cooling power but also severely limits the device’s operational temperature range. Our study highlights quantum dots as efficient platforms for magnon-driven refrigeration, offering valuable insights for spintronic and quantum technologies.

We investigate the time evolution of Kondo systems following a quench in the Hamiltonian parameters. In the case of the single-channel Kondo model coupled to a normal metallic bath, we identify universal behavior in the Loschmidt echo, with the characteristic time scale set by the inverse Kondo temperature. For the two-channel Kondo model, we analyze quenches that drive the system toward a non-Fermi liquid state and examine the corresponding dynamical features. Finally, we consider a magnetic impurity coupled to an s-wave superconducting bath. We predict that superconducting correlations strongly suppress deviations from the initial doublet state and hinder the dynamical formation of the Kondo singlet. Rich dynamical behavior also emerges near the quantum critical point, where the return rate function exhibits signatures of a dynamical quantum phase transition.

Understanding correlated electrons remains a challenge slowing advances in Quantum Technologies. We address this challenge with synthetic topological quantum matter built with semiconductor and graphene quantum dots. We start with quantum dots in a topological insulator and describe a strain sensor based on strain induced topological to trivial transition.
We next describe quantum dots and their arrays in semiconductor nanowires and show that they potentially host Haldane and Majorana quasiparticles, macroscopic quantum states and topologically protected qubits. We describe sublattice and twist engineering of flat electronic bands, resulting in correlations and magnetism and spontaneously broken valley and spin symmetry states in bilayer quantum dots.

Electronic correlations in few-layer graphene systems such as rhombohedral ABC graphene or Bernal AB graphene enable novel Stoner and intervalley coherence correlated states. The corresponding order parameters are typically meV strong, similar to the strength of spin proximity effects—spin-orbit coupling and exchange interactions—induced by proximity to transition metal dichalcogenides and van der Waals magnetic semiconductors. I will present several examples of this interplay and outline our theoretical approach, which is based on realistic DFT-based effective single-particle Hamiltonians and generalized RPA susceptibility. In particular, I will demonstrate how the presence of valley-Zeeman spin-orbit coupling in graphene leads to new spin-valley coherence phases in the presence of electron interactions.

I acknowledge support from SPP2244 and SFB 1277.

Y. Zhumagulov et al, Phys. Rev. Lett. 132, 186401 (2025).

Solid state systems with nontrivial topology exhibit many fascinating properties that are stable under external perturbations. A prominent example are topological insulators which are insulating in the bulk but have conducting surfaces with transport on surface states whose existence is protected by the topology of the bandstructure. Among semimetals, Weyl semimetals are topological. They are characterized by the linear Weyl dispersion of electrons with a definite chirality near certain points in the Brillouin zone. These Weyl points are sources and sinks of the topological charge.

A study of photocurrents – electrical currents generated in response to homogeneous light excitation – is an efficient method of probing the topological properties of various systems. Photocurrents are allowed in non-centrosymmetric media, and their direction is determined by the system's symmetry. In Weyl semimetals, the direction of the photocurrent reverses when switching from right-handed to left-handed excitation. The value of the photocurrent in each Weyl node is proportional to its topological charge. In the semiclassical limit, where photon energies are much smaller than the mean electron energy, the value of the helicity-dependent photocurrent is determined by fundamental constants and the light frequency. We demonstrate that the microscopic mechanisms responsible for this universal photocurrent are Berry curvature and side jumps that occur during scattering by disorder. We calculate the helicity-driven photocurrent value in chiral Weyl semimetals.

Gateable semiconductor quantum dots (QDs) provide a versatile platform for analog quantum simulations of electronic many-body systems. In particular, smaller gate-defined QD arrays offer a natural representation of the π-electron system of small hydrocarbons. In this talk I will discuss the prospects for extending such analog QD simulators to encompass also the nuclear degrees of freedom by representing the molecular vibrational modes by single-mode microwave resonators. As an example, we study the gate-tunable energy transfer from voltage-biased double, and triple quantum dot systems to a single-mode resonator, which may be operated as gate-tunable micromasers emulating current-induced vibrational instabilities in single-molecule junctions. These nonequilibrium QD-cQED problems are treated theoretically by Lindblad master equations or perturbative Keldysh field theory methods, used here to uncover bifurcations to limit-cycle dynamics, entrainment to external drives and quantum mode synchronization.

We propose to analyse the frequency-dependent nonlinear Hall effect in a Dirac or Weyl semimetal (D/WSM) as a possible way to detect dark matter particles, assumed here to be massive dark photons. The dark matter is still an unidentified, albeit dominant component of the matter in the Universe, with important consequences for the cosmological models. The dark photon is one of many candidates for dark matter. It is expected to interact with the standard model photon with the coupling constant $\alpha\ll 1$. We use a kinetic equation taking into account two coupled U(1)-gauge fields, one being the standard Maxwell electromagnetic field and the other corresponding to the dark sector. The resulting non-linear currents depend on the coupling constant $\alpha$. The conservative estimate [1] shows that the technique should have a sensitivity of the order of 10$^{-9}$ and be applicable for an experimentally relevant range of masses.

[1] Marek Rogatko and Karol I. Wysokinski, Charge transport in chiral solids as a possible tool in search of dark matter signals, Phys. Rev. D 108, 104062 (2023).

Dynamical quantum phase transitions are non-analyticities in a dynamical free energy, which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here, we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeros. We show, in particular, that entering a critical region where the density of Fisher zeros is nonzero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. In one- and two-dimensional symmetry protected topological matter we further show that that cusps in the bulk return rate at critical times are associated with sudden changes in the boundary contribution to the dynamical free energy. We show that these sudden changes are related to the periodical appearance of eigenvalues close to zero in the dynamical Loschmidt matrix, in a close analogy to the equilibrium bulk-boundary correspondence. Generalisations to topological models with arbitrary topological indices, higher dimensional topological matter, and higher order topology are also discussed. In all cases we see evidence of a dynamical bulk-boundary correspondence.

The quantum Hall edge is conventionally described within the Luttinger liquid theory. This theory does not contain intrinsic energy scales, and thus predicts scale-invariant behaviour. This can be characterized via the quasiparticle property called “scaling dimension”.

Unlike the quasiparticle [fractional] charge and [fractional] statistics, the scaling dimension is not a fundamental property, but is a quantity that characterizes the quasiparticle dynamics. Nevertheless, the scale-invariant behaviour is the common property of all Luttinger-liquid models for quantum Hall edges.

Observing this behaviour is known to be problematic both in terms of achieving the qualitatively correct behaviour in experiments and quantitatively matching with theory [1], [2], [3] and has only been demonstrated in a limited number of experiments [4].

I will present recent theory [5] that enables model-independent verification of the scaling behaviour. I will further present the analysis of experimental data [6] within this theoretical framework. Our analysis clearly shows emergence of energy scales below the bulk gap that break the scaling behaviour. We further show that for small enough energies the scaling behaviour holds, yet the scaling dimension is heavily renormalized compared to naïve theory predictions.

This sheds light on the complex physics of quantum point contacts in the quantum Hall effect and opens up new avenues to investigate it.

Time permitting, I will comment on the recent results by Refs. [7], [8] that reported observing unrenormalized scaling dimension. In short, while the scaling dimension appears unrenormalized, the data of both works exhibit the scaling breakdown similar to the one we observe in Ref. [6].

[1] M. Heiblum, Quantum shot noise in edge channels, physica status solidi (b) 243, 3604 (2006), https://doi.org/10.1002/pssb.200642237.
[2] I. P. Radu et al., Quasi-Particle Properties from Tunneling in the $\nu = 5/2$ Fractional Quantum Hall State, Science 320, 899 (2008), https://doi.org/10.1126/science.1157560.
[3] S. Baer et al., Experimental probe of topological orders and edge excitations in the second Landau level, Phys. Rev. B 90, 075403 (2014), https://doi.org/10.1103/PhysRevB.90.075403.
[4] L. A. Cohen et al., Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact, Science 382, 542 (2023), https://doi.org/10.1126/science.adf9728.
[5] N. Schiller, Y. Oreg, and K. Snizhko, Extracting the scaling dimension of quantum Hall quasiparticles from current correlations, Phys. Rev. B 105, 165150 (2022), https://doi.org/10.1103/PhysRevB.105.165150.
[6] N. Schiller et al., Scaling tunnelling noise in the fractional quantum Hall effect tells about renormalization and breakdown of chiral Luttinger liquid, https://arxiv.org/abs/2403.17097.
[7] A. Veillon et al., Observation of the scaling dimension of fractional quantum Hall anyons, Nature 632, 517 (2024), https://doi.org/10.1038/s41586-024-07727-z.
[8] R. Guerrero-Suarez et al., Universal Anyon Tunneling in a Chiral Luttinger Liquid, https://arxiv.org/abs/2502.20551.

Two-dimensional moiré superlattices have emerged as ideal systems to study the many-body interactions and correlated states in topologically nontrivial energy bands. The filling factor of the moiré energy band can be changed by varying the gate voltage, while other electronic properties can be modified by easily accessible external factors such as an external electric or magnetic fields, strain or a twist angle between the atomic layers forming a moiré pattern. Fractional Chern insulators are the zero magnetic field analog of the fractional quantum Hall (FQH) effect. They appear in fractionally filled Chern bands and were recently observed in twisted MoTe2 and in rhom-bohedral graphene aligned with hexagonal boron nitride. These fractionalized states in moiré systems are expected to be in the same universality class as their counterparts in Landau levels, but the periodic potential and quantum geometry can have significant effects on physical observables. In this work, we analyze stability and optical properties of fractional Chern insulators when their quantum geometric properties differ from standard fractional quantum Hall (FQH) states in a Landau level. This can be quantified by calculation of deviation from a uniform Berry curvature or Girvin-MacDonald-Platzman (GMP) algebra. We determine ideal quantum geometry conditions where Landau-level-like correlations at long length scales are expected. Moving away from this ideal point by varying model parameters, we investigate the effect of quantum geometry on collective excitations of FCI’s and their coupling to light.

The ideal two-dimensional kagome lattice has attracted significant attention due to its characteristic electronic band structure features. Unlike the honeycomb lattice, which exhibits Dirac and saddle points, the kagome lattice also hosts an ideal flat band. This unique lattice structure corresponds to rich physics, especially in the context of electronic properties. In several compounds containing the kagome sublattice, the realization of charge density waves (CDW) at low temperatures has been reported.

First, AV3​Sb5​ (A = K, Rb, Cs) compounds are rare examples where CDW coexists with superconductivity. The CDW is realized through atom displacement within the V-kagome sublattice [1]. Second, FeGe exemplifies a case where CDW is induced by correlation-driven phonon softening, resulting in a significant modification of the Ge atom [2]. In both cases, new system symmetries can be identified through phonon spectra analyses.

Lattice dynamics can also lead to intriguing findings. For CoSn-like compounds (P6/mmm symmetry), where both kagome and honeycomb lattices are present, we have discovered chiral phonons [3]. Additionally, in some cases, imaginary soft modes are observed, leading to new symmetries. In our study, we predicted the crystal structure of RhPb with P-62m symmetry (containing a distorted kagome lattice), which was confirmed experimentally [4].

In summary, studies of lattice dynamics can be a valuable tool to confirm [5] or negate [6] the realization of structures containing kagome-like sublattices.

[1] A. Ptok, A. Kobiałka, M. Sternik, J. Łazewski, P.T. Jochym, A. M. Oleś, and P. Piekarz, Phys. Rev. B 105, 235134 (2022).
[2] A. Ptok, S. Basak, A. Kobiałka, M. Sternik, J. Łazewski, P. T. Jochym, A. M. Oleś, and P. Piekarz, Phys. Rev. Materials 8, L080601 (2024).
[3] A. Ptok, A. Kobiałka, M. Sternik, J. Łazewski, P. T. Jochym, A. M. Oleś, S. Stankov, and P. Piekarz, Phys. Rev. B 104, 054305 (2021).
[4] A. Ptok, W.R. Meier, A. Kobiałka, S. Basak, M. Sternik, J. Łażewski, P.T. Jochym, M.A. McGuire, B.C. Sales, H. Miao, P. Piekarz, and A.M. Oleś, Phys. Rev. Research 5, 043231 (2023).
[5] S. Basak and A. Ptok, Materials 16, 78 (2023).
[6] A. Ptok, Physical Review B 109, 216501 (2024).

Entanglement entropy and its scaling properties have recently emerged as a way to classify states of matter. Measuring entanglement usually relies on full state tomography and requires exponentially large resources. To circumvent this complexity, a connection between entanglement entropy and fluctuations of conserved observables has been established and tested for systems and states exhibiting volume-law, area-law, and logarithmic scaling of entanglement [1]. Here we generalize this approach to non-conserved quantities and introduce reduced fluctuations, which can reveal the scaling properties of entanglement even when the symmetries of the system are broken [2]. We present this approach using numerical results for the spin-$1/2$ $XYZ$ model.

[1] K. Pöyhönen, A. G. Moghaddam, and T. Ojanen, Phys. Rev. Res. 4, 023200 (2022).
[2] S. Głodzik, A. G. Moghaddam, K. Pöyhönen, T. Ojanen, arXiv 2412.15765

Large electron densities are known to increase the significance of interactions, which often leads to instabilities in the simple Fermi liquid state. One way to achieve high electron densities is to tune the system to exhibit a Van Hove singularity (VHS) close to the Fermi level. VHSs are particularly pronounced in systems of reduced dimensionality. We propose an experimental setup consisting of an adatom positioned between two zigzag graphene nanoribbons (ZGNRs) [1] and coupled to the edge states in the topological Zak phase [2], where our numerical renormalization group theory predicts interesting interplay between Kondo effect and the multipied VHSs. We demonstrate that by using the known evolution of the ZGNR spectrum with transverse electric fields into a half-metallic state, one can tune the types and positions of VHSs in each spin channel. This provides an exotic electronic bath for a magnetic adatom. In particular, due to the power-law diverging density of states in the nanoribbon, the Kondo temperature is strongly enhanced, but the usual Kondo peak in local spectrum is replaced by a power-law pseudo-gap, which could be observed e.g. through scanning tunneling spectroscopy. We will present predictions for even more exotic situations that can be accessed by tuning electric fields. Our goal is to motivate experimental efforts in this direction.

[1] Y.-W. Son, M. L. Cohen and S. G. Louie, Nature 347, 444 (2006).
[2] P. Delplace, D. Ullmo, G. Montambaux, Phys. Rev. B 84, 195452 (2011).

Acknowledgements:
This work has been supported by National Science Centre in Poland through grant no. 2023/51/D/ST3/00532

One of the challenges in diagrammatic simulations of nonequilibrium phenomena in lattice models is the large memory demand for storing momentum-dependent two-time correlation functions. This problem can be overcome with the recently introduced quantics tensor train (QTT) representation of multivariable functions. Here, we demonstrate nonequilibrium Green's function simulations with high momentum resolution, up to times which exceed the capabilities of standard implementations and are long enough to study, e.g., thermalization dynamics and transient Floquet physics during multi-cycle electric field pulses (arXiv:2412.14032). The self-consistent calculation on the three-leg Kadanoff-Baym contour employs only QTT-compressed functions, and input functions which are either generated directly in QTT form, or obtained via quantics tensor cross interpolation.

Multi-terminal Josephson junctions emerge in theory and experiment as versatile devices compatible with current quantum computing devices. Apart from theoretical predictions of non-trivial topologies [1], their basic and readily available architectures already allow the construction of efficient supercurrent diodes [2]. While in most theoretical and experimental works the central scattering region is structureless, we argue in [3] that by inserting a single electronic level, the supercurrent diode effect can be significantly enhanced [3]. A great advantage of such an architecture is that the underlying BCS gauge symmetry can be exploited to simplify its description down to a certain two-terminal analog. The powerful mapping of Ref. [3] ensures that devices with the same total hybridization of the leads with the central electronic level represent the same family that can be treated using the same input in an analytic way.

Consequently, this reduces the numerical resources required to optimize such devices in terms of the efficacy of the supercurrent diode effect. In this talk, we present such a study and show simple guidelines for their optimization in terms of maximizing the diode effect. Finally, using the three-terminal single level set-up, we derive a simple universal relation for completely switching off such a device. The condition is analytical and requires only certain geometrical properties of the device to be fulfilled. Its universality is moreover manifestly temperature and correlation independent. The resulting switching characteristic therefore allows for the construction of a supercurrent transistor switch of nanoscopic dimensions. We provide a corresponding device design based on existing 2DEG fabrication technology.

[1] R. L. Klees et al., Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter, Phys. Rev. Lett. 124, 197002 (2020).
[2] M. Coraiola et al., Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction, ACS Nano, Vol 18, Issue 12 (2024)
[3] P. Zalom, M. Žonda, and T. Novotný, Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions, Phys. Rev. Lett. 132, 126505 (2024).

Despite being well known for its strong anti-ferromagnetic correlations, under the right conditions, the Fermi-Hubbard model can also host ferromagnetism. Here, we explore two phenomena that drive the system on different geometries to ferromagnetic states, the Nagaoka effect at extreme interaction strengths on the triangular and square lattices, and the flat band physics on the Kagome lattice. We study short-range spin correlations and other thermodynamic properties at finite temperatures using numerically exact methods and identify the regions with dominant ferromagnetic correlations in each case. We also discuss the relevance of our results to recent observations with ultracold atoms in optical lattices.

Ferromagnetic resonance is used to reveal features of the buried electronic band structure at interfaces between ferromagnetic metals and topological insulators [1]. By monitoring the evolution of magnetic damping, the application of this method to a hybrid structure consisting of a ferromagnetic layer and a 3D topological insulator reveals a clear fingerprint of the Dirac point and exhibits additional features of the interfacial band structure not otherwise observable. The underlying spin-pumping mechanism is discussed in the framework of dissipation of angular momentum by topological surface states (TSSs). Tuning of the Fermi level within the TSS was verified both by varying the stoichiometry of the topological insulator layer and by electrostatic backgating and the damping values obtained in both cases show a remarkable agreement. The high-energy resolution of this method additionally allows us to resolve the energetic shift of the local Dirac points generated by local variations of the electrostatic potential. Calculations based on the chiral tunneling process naturally occurring in TSSs agree well with the experimental results.

[1] Pietanesi et al., “Tracing Dirac points of topological surface states by ferromagnetic resonance”, Phys. Rev. B 109, 064424 (2024)

The analysis of quantum dynamics in large interacting systems is a challenging task due to the complexity of the Hilbert space. This challenge is particularly significant when resolving specific energy scales imposed by external potentials. We demonstrate that the fermionic truncated Wigner approximation (fTWA) and its variants can yield unexpectedly accurate results in simulations of one- and two-dimensional fermionic systems. The computational efficiency of this semiclassical method enables the exploration of systems with hundreds of lattice sites, allowing for the investigation of regimes relevant to realistic experiments. Our discussion focuses on both disordered and disorder-free potentials, which have been extensively studied in optical lattice experiments.

Decoherence is usually cast as the nemesis of entanglement in open quantum systems. Here we overturn that narrative and show that environmental engineering can, by itself, generate and stabilize entanglement. We analyse two bosonic modes, each coupled to an independent, uncorrelated thermal bath, and explore two complementary routes toward autonomous entanglement: (i) direct mode–mode coupling and (ii) dissipation-induced single-mode squeezing followed by passive linear optics [1].
Going beyond previous Markov-limit studies that dismissed the possibility of steady-state entanglement by neglecting anomalous coupling terms [2], we perform a full non-equilibrium treatment that embraces non-Markovian noise and counter-rotating interactions. Logarithmic negativity reveals sizeable, robust entanglement in both scenarios
Our results depicts an experimentally realistic blueprint—compatible with contemporary photonic circuitry [3]—for turning unavoidable dissipation into a functional resource. By revealing how tailored system-bath couplings autonomously drive quantum correlations, this work enriches the toolbox of reservoir engineering and advances the quest for scalable, self-contained quantum technologies.

[1] M. M. Wolf, J. Eisert, and M. B. Plenio, Phys. Rev. Lett. 90, 047904 (2003).
[2] B. Longstaff, M. G. Jabbour, and J.B. Brask, Phys. Rev. A, 108, 032209 (2023).
[3] J. Laurat et al J. Opt. B: Quantum Semiclass. Opt. 7, S577 (2005).

We present a comprehensive analysis of the magnetic excitations and electronic properties of fully quantum double-exchange ferromagnets, i.e., systems where ferromagnetic ordering emerges from the competition between spin, charge, and orbital degrees of freedom, but without the canonical approximation of using classical localized spins. Specifically, we investigate spin excitations within the Kondo lattice-like model, as well as a two-orbital Hubbard Hamiltonian in the orbital-selective Mott phase. The magnon dispersion, damping, and spectral weight computational analysis of these models reveal unexpected phenomena, such as magnon mode softening and the anomalous decoherence of magnetic excitations as observed in earlier experimental efforts, but without the need of using phononic degrees of freedom. We show that these effects are intrinsically linked to incoherent spectral features near the Fermi level, which arise due to the quantum nature of the local (on-site) triplet. This incoherent spectrum leads to a Stoner-like continuum on which spin excitations scatter, governing magnon lifetime and strongly influencing the dynamical spin structure factor. By varying the electron density, our study explores the transition from coherent to incoherent magnon spectra. Furthermore, we demonstrate that the magnitude of the localized spin mitigates decoherence by suppressing the incoherent spectral contributions near the Fermi level. Finally, we show that this behavior is also present in multi-orbital models with partially filled orbitals, namely in systems without localized spin moments, provided the model is in a large coupling strength regime. Our results potentially have far-reaching implications for understanding ferromagnetic ordering in a wide variety of multi-band systems. These findings establish a previously unknown direct connection between electronic correlations and spin excitations in those materials.