Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 004, 15 pages      arXiv:1101.0035      https://doi.org/10.3842/SIGMA.2011.004
Contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”

Correlation Function and Simplified TBA Equations for XXZ Chain

Minoru Takahashi
Fachbereich C Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

Received September 27, 2010, in final form December 27, 2010; Published online January 08, 2011

Abstract
The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's multiple integral formula for the general correlations is derived. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ς(3),ς(5),ς(7),.... We can calculate density sub-matrix of successive seven sites. Entanglement entropy of seven sites is calculated. These methods can be extended to XXZ chain up to n=4. Correlation functions are expressed by the generalized zeta functions. Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different with Yang-Yang type TBA equations and contains only one unknown function. This equation is very useful to get the high temperature expansion. In this paper we get the analytic solution of this equation at Δ=0.

Key words: thermodynamic Bethe ansatz equation; correlation function.

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