Topological Field Theory far from Equilibrium

TL;DR

This paper extends the application of topological field theories to non-equilibrium quantum systems, demonstrating that driven open dynamics can exhibit topological properties similar to equilibrium states, including chiral edge modes.

Contribution

It constructs a model of a driven open quantum system with a Chern insulator steady state and shows that a Chern-Simons theory describes its response, extending topological field theory to non-equilibrium.

Findings

Chern-Simons theory describes the response of the non-equilibrium system.

Chiral edge modes are stabilized by dissipative bulk.

Topological properties persist far from equilibrium.

Abstract

The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional driven open dynamics with a Chern insulator steady state. Within a Keldysh field theory approach, we show that under mild assumptions - particle number conservation and purity of the stationary state - an abelian Chern-Simons theory describes its response to external perturbations. As a corollary, we predict chiral edge modes stabilized by a dissipative bulk.