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Painlevé transcendent describes quantum correlation function of the XXZ antiferromagnet away from the free-fermion point. (English) Zbl 0904.34010
Summary: The authors consider quantum correlation functions of the antiferromagnetic spin-1 2 Heisenberg XXZ spin chain in a magnetic field. For a magnetic field close to the critical field h c (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of a solution of the Painlevé V transcendent. This establishes a relation between solutions to Painlevé differential equations and quantum correlation functions in models of interacting fermions. Painlevé transcendents are known to describe correlation functions in models with free fermionic spectra.
MSC:
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
82D40Magnetic materials (statistical mechanics)
34M55Painlevé and other special equations; classification, hierarchies