A duality principle for the multi-block entanglement entropy of free fermion systems



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Carrasco, J. A. and Finkel Morgenstern, Federico and González López, Artemio and Tempesta, Piergiulio (2017) A duality principle for the multi-block entanglement entropy of free fermion systems. Scientific reports, 7 . ISSN 2045-2322

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Official URL: http://dx.doi.org/10.1038/s41598-017-09550-1


The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set A of sites of the subsystem considered and the set K of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets A and K to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets A and K consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and r-partite information generalizing the known ones for the single block case.

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© The Author(s) 2017.
Tis work was partially supported by Spain’s MINECO under research grant no. FIS2015-63966-P. PT has been partly supported by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO, Spain). JAC would also like to acknowledge the fnancial support of the Universidad Complutense de Madrid through a 2015 predoctoral scholarship.

Uncontrolled Keywords:Spin chain; Toeplitz determinants
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:45351
Deposited On:08 Nov 2017 18:13
Last Modified:10 Dec 2018 15:09

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