A bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors

TL;DR

This paper investigates the relationship between dynamical quantum phase transitions and boundary effects in one-dimensional topological insulators and superconductors, revealing a bulk-boundary correspondence through Loschmidt echo analysis.

Contribution

It introduces a bulk-boundary correspondence for dynamical phase transitions in 1D topological systems using Loschmidt echo and boundary contributions.

Findings

Cusps in the bulk return rate are linked to boundary changes.

Eigenvalues near zero in the Loschmidt matrix correlate with boundary effects.

Long-range entanglement between edges is periodically created during transitions.

Abstract

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 tc are associated with sudden changes in the boundary contribution. For our 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.