Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators

TL;DR

This paper explores how mirror symmetry in topological crystalline insulators protects certain dynamical quantum phase transitions during quantum quenches, introducing new topological order parameters and demonstrating these phenomena in lattice models.

Contribution

It reveals that mirror symmetry can protect DQPTs in high-dimensional topological systems and introduces dynamical topological order parameters for these transitions.

Findings

Mirror symmetry creates symmetry-protected DQPTs in topological insulators.

DQPTs can be characterized by a reduced rate function.

Demonstration of DQPTs in lattice models of topological crystalline insulators.

Abstract

Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-dimensional chiral-symmetric systems with mirror symmetry. Mirror-symmetry-protected DQPTs can be easily captured by a reduced rate function. Moreover, we introduce dynamical topological order parameters for mirror-symmetry-protected DQPTs. Finally, we demonstrate DQPTs using lattice models for a time-reversal invariant topological crystalline insulator and a higher-order topological insulator.