Differential equation for a correlation function of the spin- 1 2 Heisenberg chain

Holger Frahm; Alexander R. Its; Vladimir E. Korepin

doi:10.1016/0550-3213(94)90370-0

Differential equation for a correlation function of the spin- 1 2 Heisenberg chain

Holger Frahm
, Alexander R. Its
, Vladimir E. Korepin

Stony Brook University

Leibniz University Hannover
Indiana University-Purdue University Indianapolis

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

7 Scopus citations

Abstract

We consider the probability to find a string of x adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation function is a τ-function of this system.

Original language	English
Pages (from-to)	694-710
Number of pages	17
Journal	Nuclear Physics, Section B
Volume	428
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(94)90370-0
State	Published - Oct 17 1994

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title = "Differential equation for a correlation function of the spin- 1 2 Heisenberg chain",

abstract = "We consider the probability to find a string of x adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation function is a τ-function of this system.",

author = "Holger Frahm and Its, \{Alexander R.\} and Korepin, \{Vladimir E.\}",

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T1 - Differential equation for a correlation function of the spin- 1 2 Heisenberg chain

AU - Frahm, Holger

AU - Its, Alexander R.

AU - Korepin, Vladimir E.

PY - 1994/10/17

Y1 - 1994/10/17

N2 - We consider the probability to find a string of x adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation function is a τ-function of this system.

AB - We consider the probability to find a string of x adjacent parallel spins in the antiferromagnetic ground state of the model (in a magnetic field). We derive a system of integro-difference equations which define this probability. This system is completely integrable, it has Lax representation and a corresponding Riemann-Hilbert problem. The quantum correlation function is a τ-function of this system.

UR - https://www.scopus.com/pages/publications/0008069975

U2 - 10.1016/0550-3213(94)90370-0

DO - 10.1016/0550-3213(94)90370-0

M3 - Article

SN - 0550-3213

VL - 428

SP - 694

EP - 710

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -

Differential equation for a correlation function of the spin- 1 2 Heisenberg chain

Abstract

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