Mutual information for fermionic systems

TL;DR

This paper investigates the behavior of mutual information in various quadratic fermionic chains, revealing how it correlates with area law violations, model parameters, and the structure of entanglement, with implications for quantum information theory.

Contribution

It provides a comprehensive analysis of mutual information across different fermionic models, highlighting non-universal features and the impact of long-range interactions and pairing on entanglement.

Findings

Mutual information increases monotonically with the conformal four-point ratio in cases of logarithmic area law violation.

Non-monotonic behavior of MI observed when non-logarithmic violations occur, indicating complex entanglement structures.

In the volume law case, MI vanishes entirely, showing a distinct entanglement pattern.

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.