Dynamical topological invariants and reduced rate functions for dynamical quantum phase transitions in two dimensions

TL;DR

This paper introduces a dynamical topological invariant and reduced rate function to characterize two-dimensional dynamical quantum phase transitions, linking topological features in momentum space with non-analyticities in the Loschmidt echo.

Contribution

It defines a new dynamical topological invariant along a contour in momentum space and connects 2D DQPTs with 1D invariants, providing a novel framework for analysis.

Findings

Dynamical topological invariant reflects vorticity of dynamical vortices.

Reduced rate function captures non-analyticities at critical times.

Application to Haldane and quantum anomalous Hall models demonstrates experimental relevance.

Abstract

We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of two-dimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in momentum space. Such a dynamical topological invariant reflects the vorticity of dynamical vortices responsible for the DQPTs, and thus serves as a dynamical topological order parameter in two dimensions. We demonstrate that when the contour crosses topologically protected fixed points in the quench dynamics, an intimate connection can be established between the dynamical topological order parameter in two dimensions and those in one dimension. We further define a reduced rate function of the Loschmidt echo on the contour, which features non-analyticities at critical times and is sufficient to characterize DQPTs in two dimensions. We illustrate our results using the Haldane honeycomb model and the quantum anomalous Hall model as concrete examples, both of which have been experimentally realized using cold atoms.