Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermions

L Brightmore, G P Gehér*, A R Its, V E Korepin, F Mezzadri, M Y Mo, J A Virtanen

*Corresponding author for this work

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Abstract

We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, arXiv:1104.1004, for the reduced density of states of two disjoint intervals with lattice sites P={1,2,...,m}\cup{2m+1,2m+2,..., 3m}, which applies to this model. As a first step in the asymptotic analysis of this system, we consider its simplification to two disjoint intervals separated just by one site, and we rigorously calculate the mutual information between these two blocks and the rest of the chain. In order to compute the entropy we need to study the asymptotic behaviour of an inverse Toeplitz matrix with Fisher-Hartwig symbol using the the Riemann--Hilbert method.
Original languageEnglish
Article number345303
Number of pages32
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number34
Early online date15 Jun 2020
DOIs
Publication statusPublished - 3 Aug 2020

Keywords

  • quantum spin chain
  • quantum entanglement entropy
  • mutual information
  • Riemann-Hilbert problems

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