Mutual information for fermionic systems

Lepori, Luca; Paganelli, Simone; Franchini, Fabio; Trombettoni, Andrea (2022) Mutual information for fermionic systems. Physical Review Research, 4 (3). ISSN 2643-1564

PDF - Published Version - article
Available under License Creative Commons Attribution.
Download (1MB)

Official URL: http://doi.org/10.1103/PhysRevResearch.4.033212

Abstract

We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is - logarithmically or non-logarithmically - violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where non-logarithmic violations of the area law are present, non-monotonic features can be observed in the MI and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a non-universal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x -> 0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the AdS/CFT correspondence in the strong coupling limit is presented.

Item Type:

Article

Uncontrolled Keywords:

Mutual Information; Fermionic chains

Subjects:

NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Condensed Matter Physics

Divisions:

Theoretical Physics Division

Projects: