Topological gauge theory for mixed Dirac stationary states in all dimensions

TL;DR

This paper develops a universal topological gauge theory for mixed fermionic states across all dimensions, revealing new quantized responses and extending topological concepts to non-equilibrium quantum systems.

Contribution

It introduces a universal real-time U(1) topological gauge field action for mixed states, independent of equilibrium conditions, and connects topological responses with non-equilibrium physics.

Findings

Derives a universal gauge action applicable in all dimensions.

Identifies quantized nonlinear responses in mixed states.

Extends anomaly inflow and bulk-boundary correspondence to non-equilibrium systems.

Abstract

We derive the universal real time $U(1)$ topological gauge field action for mixed quantum states of weakly correlated fermions in all dimensions, and demonstrate its independence of the underlying equilibrium or non-equilibrium nature of dynamics stabilizing the state. The key prerequisites are charge quantization and charge conservation. The gauge action encodes non-quantized linear responses as expected for mixed states, but also quantized non-linear responses, associated to mixed state topology and accessible in experiment. Our construction furthermore demonstrates how the physical pictures of anomaly inflow and bulk-boundary correspondence extend to non-equilibrium systems.