Painlevé Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

Details Painlevé Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point Painlevé Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

1996-04-25

arxiv.org/abs/solv-int/9604005v1

J.Phys.A29:5619-5626,1996

Physics

Condensed Matter

10 pages, LaTeX2e

Scientific paper

10.1088/0305-4470/29/17/032

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that 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 the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.

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