Seminarium Fizyki Materii Skondensowanej

We study dynamical quantum phase transitions following quenches in one- and two-dimensional symmetry protected topological matter. For quenches where dynamical quantum phase transitions occur, we find that cusps in the bulk return rate at critical times are associated with sudden changes in the boundary contribution to the dynamical free energy (the return rate). For our first main example, the Su-Schrieffer-Heeger model, we show that these sudden changes are related to the periodical appearance of two eigenvalues close to zero in the dynamical Loschmidt matrix, in. a close analogy to the equilibrium bulk-boundary correspondence. We demonstrate, furthermore, that the structure of the Loschmidt spectrum is linked to the periodic creation of long-range entanglement between the edges of the system. Generalisations to topological models with arbitrary topological indices, higher dimensional topological matter, and higher order topology, and connections to order parameters are also discussed. In all cases we see evidence of a dynamical bulk-boundary correspondence.