Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain

Dmitri A. Ivanov; Alexander G. Abanov

doi:10.1088/1751-8113/47/1/015001

Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain

Dmitri A. Ivanov
, Alexander G. Abanov

Physics and Astronomy

Swiss Federal Institute of Technology Zurich
University of Zurich

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

Abstract

Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlevé equations. We present explicit results up to the 11th order and compare them with a numerical example.

Original language	English
Article number	015001
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	47
Issue number	1
DOIs	https://doi.org/10.1088/1751-8113/47/1/015001
State	Published - Jan 10 2014

Keywords

Fisher-Hartwig conjecture
full counting statistics
Painleve equations
spin chains
Toeplitz matrices

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10.1088/1751-8113/47/1/015001

Cite this

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title = "Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain",

abstract = "Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlev{\'e} equations. We present explicit results up to the 11th order and compare them with a numerical example.",

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AU - Ivanov, Dmitri A.

AU - Abanov, Alexander G.

PY - 2014/1/10

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N2 - Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlevé equations. We present explicit results up to the 11th order and compare them with a numerical example.

AB - Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painlevé equations. We present explicit results up to the 11th order and compare them with a numerical example.

KW - Fisher-Hartwig conjecture

KW - full counting statistics

KW - Painleve equations

KW - spin chains

KW - Toeplitz matrices

UR - https://www.scopus.com/pages/publications/84890635789

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DO - 10.1088/1751-8113/47/1/015001

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SN - 1751-8113

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 1

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ER -

Fisher-Hartwig expansion for the transverse correlation function in the XX spin-1/2 chain

Abstract

Keywords

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