Shachar Fraenkel
(Tel Aviv University)
 

Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this talk, I will present exact analytical results concerning entanglement within the steady state of free fermions that occupy a one-dimensional lattice containing a noninteracting impurity, and that are subjected to an external bias by two edge reservoirs. I will show that two subsystems located on opposite sides of the impurity, and within a similar distance from it, exhibit volume-law entanglement regardless of their separation, as measured by their fermionic negativity. The mutual information of the subsystems, which quantifies the total (classical and quantum) correlations between them, follows a similar scaling. This behavior arises whenever the energy distribution functions of the two edge 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). The extensive terms of the negativity and mutual information feature a simple and universal functional dependence on the scattering probabilities associated with the impurity, a functional dependence which has a clear interpretation in terms of the coherence generated between the transmitted and reflected parts of scattered wavepackets. To the extent that time permits, I will discuss further exact results for the subleading corrections to these asymptotic expressions in the case of zero temperature.

 

References:

Shachar Fraenkel and Moshe Goldstein, SciPost Phys. 15, 134 (2023)

Shachar Fraenkel and Moshe Goldstein, arXiv:2310.16901 (2023)

Shachar Fraenkel and Moshe Goldstein, arXiv:2312.XXXXX (in preparation)