Shachar Fraenkel, Tel Aviv University

Extensive long-range entanglement in a nonequilibrium steady state

Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We analytically study entanglement in the steady state of noninteracting fermions, occupying a one-dimensional lattice that hosts a generic scatterer at its center and is coupled at its ends to two biased reservoirs. 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. The mutual information of the intervals, which quantifies the total correlations between them, follows a similar scaling. We find that this behavior arises whenever the occupation functions of the two reservoirs differ, thus capturing both the case of a chemical-potential bias and the case of a temperature bias (as well as any combination of the two). By deriving exact expressions for the extensive terms of the negativity and mutual information, we prove their simple and universal functional dependence on the scattering probabilities associated with the scatterer. This simple dependence allows to demonstrate that the strong long-range entanglement is generated by the coherence between the transmitted and reflected parts of propagating particles within the energy window of the bias.

This contribution is based on arXiv:2205.12991, as well as on newer results.