Topological gauge theory for mixed Dirac stationary states in all dimensions
Ze-Min Huang, Xiao-Qi Sun, Sebastian Diehl
Abstract
We derive the universal real-time $\text{U}(1)$ topological gauge field action for mixed Dirac states of fermions, described by a density matrix weighted by a gapped Dirac operator, in all dimensions. The key prerequisites are charge quantization and charge conservation; in fact, charge quantization is the root of the action's topological properties. The gauge action encodes nonquantized linear responses as expected for mixed states, but also quantized nonlinear responses, which are accessible in experiment. Our construction furthermore demonstrates how the physical pictures of anomaly inflow and bulk-boundary correspondence extend to nonequilibrium systems. Finally, we demonstrate the independence of the gauge action of the underlying equilibrium or nonequilibrium nature of dynamics stabilizing the state.