Interacting Symmetry-Protected Topological Phases Out of Equilibrium

TL;DR

This paper develops a nonequilibrium topological classification for quantum many-body systems, revealing how topology constrains their dynamics and affects observable features like edge modes under external noise.

Contribution

It introduces a nonequilibrium topological classification framework based on unitary evolution, extending equilibrium concepts to far-from-equilibrium quantum dynamics.

Findings

Topologically protected edge modes are robust against noise in nontrivial phases.

The classification predicts universal dynamical behaviors in isolated quantum systems.

External noise broadens spectral peaks only in trivial phases.

Abstract

The topological features of quantum many-body wave functions are known to have profound consequences for the physics of ground-states and their low-energy excitations. We describe how topology influences the dynamics of many-body systems when driven far from equilibrium. Our results are succinctly captured by a nonequilibrium topological classification that can be used to predict universal aspects of generic isolated quantum systems as they evolve unitarily in time. By analogy to the classifications used to describe systems in equilibrium, we consider two short-ranged entangled wave functions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. We demonstrate that this definition captures the salient features of these systems in a broad range of nonequilibrium scenarios. As well as providing conceptual insights into the constraints imposed by topology on many-body dynamics, we discuss the practical implications of our findings. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the nonequilibrium classification.