Extensive Long-Range Entanglement in a Nonequilibrium Steady State

Abstract

Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of noninteracting fermions at zero temperature in the presence of a scatterer. We show that disjoint intervals located on opposite sides of the scatterer, and within similar distances from it, maintain volume-law entanglement regardless of their separation, as measured by their fermionic negativity and coherent information. The mutual information of the intervals, which quantifies the total correlations between them, follows a similar scaling. Interestingly, this scaling entails in particular that if the position of one of the intervals is kept fixed, then the correlation measures depend non-monotonically on the distance between the intervals. By deriving exact expressions for the extensive terms of these quantities, we prove their simple functional dependence on the scattering probabilities, and demonstrate that the strong long-range entanglement is generated by the coherence between the transmitted and reflected parts of propagating particles within the bias-voltage window. The generality and simplicity of the model suggest that this behavior should characterize a large class of nonequilibrium steady states.

5 pages, 3 figures + Supplemental Material. v2: Published version, 10+10 pages, 3+2 figures; the discussion of logarithmic corrections was removed, and is now elaborated separately in arXiv:2310.16901

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• System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state
• Entanglement in dual unitary quantum circuits with impurities
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• Dissipation enables robust extensive scaling of multipartite correlations
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Entanglement transitions in a boundary-driven open quantum many-body system
• Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems