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Zbl 0904.34010
Essler, F.H.L.; Frahm, H.; Its, A.R.; Korepin, V.E.
Painlevé transcendent describes quantum correlation function of the XXZ antiferromagnet away from the free-fermion point. (English)
[J] J. Phys. A, Math. Gen. 29, No.17, 5619-5626 (1996). ISSN 0305-4470

Summary: The authors consider quantum correlation functions of the antiferromagnetic spin-${1\over 2}$ 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 2000:: *34A25 Analytical theory of ODE
82D40 Magnetic materials
34M55 Painlevé and other special equations

Keywords: quantum correlation functions; antiferromagnetic spin-${1\over 2}$ Heisenberg XXZ spin chain; magnetic field; Painlevé V transcendent; interacting fermions; fermionic spectra

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