Continued fraction TBA and functional relations in XXZ model at root of unity
Abstract
Thermodynamics of the spin 1/2 XXZ model is studied in the critical regime using the quantum transfer matrix (QTM) approach. We find functional relations indexed by the Takahashi-Suzuki numbers among the fusion hierarchy of the QTM's (T-system) and their certain combinations (Y-system). By investigating analyticity of the latter, we derive a closed set of non-linear integral equations which characterize the free energy and the correlation lengths for both <sigma_j^{+} sigma_i^{-}> and <sigma_j^{z} sigma_i^{z}> at any finite temperatures. Concerning the free energy, they exactly coincide with Takahashi-Suzuki's TBA equations based on the string hypothesis. By solving the integral equations numerically the correlation lengths are determined, which agrees with the earlier results in the low temperature limit.
Keywords
Cite
@article{arxiv.math/9803056,
title = {Continued fraction TBA and functional relations in XXZ model at root of unity},
author = {Atsuo Kuniba and Kazumitsu Sakai and Junji Suzuki},
journal= {arXiv preprint arXiv:math/9803056},
year = {2019}
}
Comments
28pages,LaTeX2.09, 9 eps files. To be published in Nucl. Phys. B