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

Thermodynamics of the spin 12 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 QTMʹs (T-system) and their certain combinations (Y-system). By investigating analyticity of the latter, we derive a closed set of nonlinear integral equations which characterize the free energy and the correlation lengths for both 〈σj+ σi−〉 and 〈σjz σiz〉 at any finite temperatures. Concerning the free energy, they exactly coincide with Takahashi-Suzukiʹs 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. © 1998 Elsevier Science BX