Topological gauge theory for mixed Dirac stationary states in all dimensions

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.

6+16 pages, 1 figure

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• Coherent information as a mixed-state topological order parameter of fermions
• Finite-temperature topological invariant for higher-order topological insulators
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Diffusion in quantum state preparation: From passive cooling to system-bath engineering