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

Abstract

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 Painlevé V transcendent. This establishes a relation between solutions of Painlevé differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlevé transcendents were known to describe correlation functions in models with free fermionic spectra.

10 pages, LaTeX2e

References in corpus (2)

• Determinant Representations for Correlation Functions of Spin-1/2 XXX and XXZ Heisenberg Magnets
• Integro-Difference Equation for a correlation function of the spin-$\frac{1}{2}$ Heisenberg XXZ chain

Cited by in corpus (11)

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• Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain
• Operator-valued Riemann-Hilbert problem for correlation functions of the XXZ spin chain
• The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model
• Normal Ordering in the Theory of Correlation Functions of Exactly Solvable Models
• Two-point correlation functions in perturbed minimal models
• Connection problem of the first Painlevé transcendents with large initial data
• Asymptotic form of two-point correlation function of the XXZ spin chain