Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

TL;DR

This paper investigates the stability of dynamical quantum phase transitions in quenched topological insulators, analyzing effects of multi-band structures and disorder, and providing criteria and numerical insights into their occurrence.

Contribution

It extends the understanding of DQPTs to multi-orbital and disordered systems, offering criteria and counterexamples, and explores the order of limits in disordered quenched topological systems.

Findings

Derived criteria for DQPTs in all spatial dimensions.

Constructed counterexamples in multi-band topological insulators.

Numerical simulations of quenched disordered topological systems.

Abstract

Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multi-band to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder.