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.
Highlights
Topology plays an important role in the characterization of quantum phases in condensed matter physics [1,2,3,4]
We introduce symmetry-protected Dynamical quantum phase transitions (DQPTs) in two-band insulators according to Ref. [43], they can be extended to multiband systems with one occupied band [45,56]
We studied DQPTs protected by mirror symmetry and elucidated the relationship between the Loshcmidt amplitudes and the crystalline topology
Summary
Topology plays an important role in the characterization of quantum phases in condensed matter physics [1,2,3,4]. Dynamical topological order parameters (DTOPs) can be defined to characterize the real time dynamics [46,47,48,49]. Previous works revealed that DQPTs in band insulators are predictable if quenches cross topological phase transitions in two-dimensional (2D) class A and 1D class AIII [43,45]. We propose DQPTs topologically characterized by mirror symmetry and clarify the conditions in some mirror-symmetric classes. We investigate DTOPs to characterize DQPTs in mirror-symmetric topological phases.
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