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)
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.