A Dynamical Bulk-Boundary Correspondence for Dynamical Quantum Phase Transitions in Topological Matter

We study the Loschmidt echo for quenches in open one-dimensional lattice models with symmetry protected topological phases. For quenches where dynamical quantum phase transitions do occur we find that cusps in the bulk return rate at critical times are associated with sudden changes in the boundary contribution. 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. 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 more general systems, higher dimensional topological matter, and higher order topology are also discussed.