Painlevé transcendent describes quantum correlation function of the XXZ antiferromagnet away from the free-fermion point

authored by: F. H.L. Essler, H. Frahm, A. R. Its, V. E. Korepin
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 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 interacting fermions. Painlevé transcendents were known to describe correlation functions in models with free fermionic spectra.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): University of Oxford
Indiana University-Purdue
Kyoto University
Stony Brook University (SBU)
Russian Academy of Sciences (RAS)
Type: Article
Journal: Journal of Physics A: Mathematical and General
Volume: 29
Pages: 5619-5626
No. of pages: 8
ISSN: 0305-4470
Publication date: 01.12.1996
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Mathematical Physics, Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.1088/0305-4470/29/17/032 (Access: Unknown)