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Journal of Mathematical Sciences

Integrable differential equations for temperature correlation functions of the XXO Heisenberg chain

Anatoli G. Izergin, Alexander Rudol'fovich Its, V. E. Korepin, N. A. Slavnov

Published Jun 1, 1996• 6 citations
Publisher
DOI
10.1007/bf02362774

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We consider isotropic XY model in the transverse magnetic field on the one dimensional lattice. Another name of the model in Heisenberg XXO model of spin 1/2.We solved long standing problem of evaluation of temperature correlations. We first represent correlation function in the model, by means of completely integrable differential equation. This is famous Ablowitz-Ladik lattice Nonlinear Schrodinger equation.Correlation function is the τττ function of this differential equation. We solved this equation and evaluate asymptotics.
We consider the isotropic XY model in a transverse magnetic field in one dimension. One can alternatively call this model the Heisenberg XXO antiferromagnet. We solve the problem of the evaluation of asymptotics of temperature correlations and explain the physical meaning of our result. To do this we represent the quantum correlation function as a tau function of a completely integrable differential equation. This is the well-known Ablowitz-Ladik lattice nonlinear Schr\"odinger differential equation.