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

doi:10.1088/1751-8121/ab9cf2

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 language	English
Article number	345303
Number of pages	32
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	53
Issue number	34
Early online date	15 Jun 2020
DOIs	https://doi.org/10.1088/1751-8121/ab9cf2
Publication status	Published - 3 Aug 2020

Keywords

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

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title = "Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermions",

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.",

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T1 - Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermions

AU - Brightmore, L

AU - Gehér, G P

AU - Its, A R

AU - Korepin, V E

AU - Mezzadri, F

AU - Mo, M Y

AU - Virtanen, J A

PY - 2020/8/3

Y1 - 2020/8/3

N2 - 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.

AB - 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.

KW - quantum spin chain

KW - quantum entanglement entropy

KW - mutual information

KW - Riemann-Hilbert problems

U2 - 10.1088/1751-8121/ab9cf2

DO - 10.1088/1751-8121/ab9cf2

M3 - Article (Academic Journal)

VL - 53

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 34

M1 - 345303

ER -

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

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