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.
Highlights
Uncovering general principles that describe the entanglement structure of quantum many-body systems is a fundamental challenge in statistical mechanics and quantum information science [1]
As described in the Introduction, the two main results in this paper are (i) the discovery that noninteracting, currentdriven, diffusive fermion models exhibit extensive mutual information and entanglement, and (ii) the development of a simple physical picture for how interactions effectively decohere these correlations and recover the expected area-law scaling of local equilibrium
Using the mapping of the local random circuit to diffusive fermions, we can interpret the parameter p2 as the analog of γin. This parametric separation between operator spreading dynamics and the diffusive dynamics leads to a large window of space and time where the system will display strong deviations from local equilibrium with a similar structure to the volume-law mutual information phase of the nonequilibrium attracting states (NEASs)
Summary
Uncovering general principles that describe the entanglement structure of quantum many-body systems is a fundamental challenge in statistical mechanics and quantum information science [1]. Single eigenstates with finite energy density above the ground state typically exhibit extensive entanglement entropy [6,7,8]; the mutual information of finite-temperature, thermal Gibbs (mixed) states still exhibits an area law [4]. We show that the long-time density matrix for driven noninteracting fermions is characterized by volume-law mutual information and entanglement, in distinct contrast to the entanglement properties at equilibrium. This result should generally apply to driven systems in the regime l ≪ L ≪ lφ.
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