Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-07-06
Czech.J.Phys. 52 (2002) 737-748
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, Latex ; Typo corrections and other minor changes
Scientific paper
10.1023/A:1016233911940
We study the diagonalization problem of certain discrete quantum integrable models by the method of Baxter's T-Q relation from the algebraic geometry aspect. Among those the Hofstadter type model (with the rational magnetic flux), discrete quantum pendulum and discrete sine-Gordon model are our main concern in this report. By the quantum inverse scattering method, the Baxter's T-Q relation is formulated on the associated spectral curve, a high genus Riemann surface in general, arisen from the study of the spectrum problem of the system. In the case of degenerated spectral curve where the spectral variables lie on rational curves, we obtain the complete and explicit solution of the T-Q polynomial equation associated to the model, and the intimate relation between the Baxter's T-Q relation and algebraic Bethe Ansatz is clearly revealed. The algebraic geometry of a general spectral curve attached to the model and certain qualitative properties of solutions of the Baxter's T-Q relation are discussed incorporating the physical consideration.
Lin Shao-shiung
Roan Shi-shyr
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