Speaker
Description
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.
