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

Atsuo Kuniba·Kazumitsu Sakai·Junji Suzuki
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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 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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Atsuo Kuniba, Kazumitsu Sakai, Junji Suzuki. 1998-03-13. Continued fraction TBA and functional relations in XXZ model at root of unity. https://doi.org/10.1016/s0550-3213(98)00300-9

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