Continued fraction TBA and functional relations in XXZ model at root of unity

Details Continued fraction TBA and functional relations in XXZ model at root of unity Continued fraction TBA and functional relations in XXZ model at root of unity

1998-03-13

arxiv.org/abs/math/9803056v2

Nucl. Phys. B 525 [FS] (1998) 597-626

Mathematics

Quantum Algebra

28pages,LaTeX2.09, 9 eps files. To be published in Nucl. Phys. B

Scientific paper

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 and 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.

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