# Dynamical Topological Quantum Phase Transitions for Mixed States

## TL;DR

This paper extends the concept of dynamical quantum phase transitions to mixed states at finite temperatures, revealing topological signatures through vortex-antivortex pairs in the phase, applicable to experimental systems like ultracold gases.

## Contribution

It introduces a framework for detecting topological phase transitions in mixed states during quantum dynamics, generalizing DQPTs to finite-temperature and ensemble settings.

## Key findings

- Observable phase singularities indicate topological changes.
- Topological properties can be identified without low-temperature initial states.
- Relevance demonstrated for ultracold atomic gas experiments.

## Abstract

We introduce and study dynamical probes of band structure topology in the post-quench time-evolution from mixed initial states of quantum many-body systems. Our construction generalizes the notion of dynamical quantum phase transitions (DQPTs), a real-time counterpart of conventional equilibrium phase transitions in quantum dynamics, to finite temperatures and generalized Gibbs ensembles. The non-analytical signatures hallmarking these mixed state DQPTs are found to be characterized by observable phase singularities manifesting in the dynamical formation of vortex-antivortex pairs in the interferometric phase of the density matrix. Studying quenches in Chern insulators, we find that changes in the topological properties of the Hamiltonian can be identified in this scenario, without ever preparing a topologically non-trivial or low-temperature initial state. Our observations are of immediate relevance for current experiments aimed at realizing topological phases in ultracold atomic gases.