Entanglement structure of current-driven diffusive fermion systems

TL;DR

This paper explores the entanglement structure of nonequilibrium steady states in driven diffusive fermion systems, revealing volume-law entanglement in noninteracting models and short-range entanglement in interacting, chaotic systems.

Contribution

It introduces and analyzes two toy models for quantum transport, demonstrating how entanglement properties differ with interactions and chaos in driven fermionic systems.

Findings

Noninteracting models show volume-law entanglement.

Interacting, chaotic models exhibit short-range entanglement.

Results suggest local equilibrium emergence in quantum-chaotic systems.

Abstract

When an extended system is coupled at its opposite boundaries to two reservoirs at different temperatures or chemical potentials, it cannot achieve a global thermal equilibrium and is instead driven to a set of current-carrying nonequilibrium states. Despite the broad relevance of such a scenario to metallic systems, there have been limited investigations of the entanglement structure of the resulting long-time states, in part, due to the fundamental difficulty in solving realistic models for disordered, interacting electrons. We investigate this problem by carefully analyzing two "toy" models for coherent quantum transport of diffusive fermions: the celebrated three-dimensional, noninteracting Anderson model and a class of random quantum circuits acting on a chain of qubits, which exactly maps to a diffusive, interacting fermion problem. Crucially, the random circuit model can also be tuned to have no interactions between the fermions, similar to the Anderson model. We show that the long-time states of driven noninteracting fermions exhibit volume-law mutual information and entanglement, both for our random circuit model and for the nonequilibrium steady-state of the Anderson model. With interactions, the random circuit model is quantum chaotic and approaches local equilibrium, with only short-range entanglement. These results provide a generic picture for the emergence of local equilibrium in current-driven quantum-chaotic systems, and also provide examples of stable, highly-entangled many-body states out of equilibrium. We discuss experimental techniques to probe these effects in low-temperature mesoscopic wires or ultracold atomic gases.