Mutual information for fermionic systems

• URL: http://arxiv.org/abs/2012.00045v2
• Date: Tue, 20 Sep 2022 10:05:50 GMT
• Title: Mutual information for fermionic systems
• Authors: Luca Lepori, Simone Paganelli, Fabio Franchini, and Andrea Trombettoni
• Abstract summary: We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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