The fisher-hartwig formula and entanglement entropy

A. R. Its; V. E. Korepin

doi:10.1007/s10955-009-9835-9

The fisher-hartwig formula and entanglement entropy

A. R. Its
, V. E. Korepin

Institute for Theoretical Physics

Indiana University-Purdue University Indianapolis

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.

Original language	English
Pages (from-to)	1014-1039
Number of pages	26
Journal	Journal of Statistical Physics
Volume	137
Issue number	5
DOIs	https://doi.org/10.1007/s10955-009-9835-9
State	Published - Dec 2009

Keywords

Entanglement
Fisher-Hartwig formula
Spin chain
Toeplitz determinant

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10.1007/s10955-009-9835-9

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title = "The fisher-hartwig formula and entanglement entropy",

abstract = "Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.",

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N2 - Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.

AB - Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use the Fisher-Hartwig formula, as well as the recent results concerning the asymptotics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.

KW - Entanglement

KW - Fisher-Hartwig formula

KW - Spin chain

KW - Toeplitz determinant

UR - https://www.scopus.com/pages/publications/74449083016

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DO - 10.1007/s10955-009-9835-9

M3 - Article

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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ER -

The fisher-hartwig formula and entanglement entropy

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Keywords

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