Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps

TL;DR

This paper reveals that in multi-band quantum systems, dynamical quantum phase transitions are fundamentally linked to topologically protected nodes in wavefunction overlaps, extending understanding beyond simple two-band models.

Contribution

It introduces the concept that topologically protected nodes in wavefunction overlaps are essential for DQPTs in multi-band systems, generalizing previous two-band results.

Findings

Topologically protected nodes in wavefunction overlaps induce DQPTs.

Nodes occur when initial and post-quench states have different topological indices.

Demonstrated in a three-band Hofstadter model in 1D and 2D.

Abstract

A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state---i.e. the Loschmidt echo---vanishes at critical times $\{t^{*}\}$. Analytical results so far are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this work, we show that for a general multi-band system, a robust DQPT relies on the existence of nodes (i.e. zeros) in the wavefunction overlap between the initial band and the post-quench energy eigenstates. These nodes are topologically protected if the two participating wavefunctions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.