Speaker
Description
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).
