96-160 V.E.Korepin, A.R.Its, F.H.L. Essler, H.Frahm

Painlev\'e V Differential Equation Describes Quantum Correlation Function of the XXZ Antiferromagnet outside of free-fermion point (28K, LaTex) Apr 29, 96

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Abstract. We consider quantum correlation functions of the antiferromagnetic spin- 1/2 Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e V differential equations and quantum correlation functions in models of interacting fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.

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