Algebraic Geometry and Hofstadter Type Model

Details Algebraic Geometry and Hofstadter Type Model Algebraic Geometry and Hofstadter Type Model

2002-06-11

arxiv.org/abs/math-ph/0206014v1

Int.J.Mod.Phys. 16 (2002) 2097-2106

Physics

Mathematical Physics

9 pages, Latex; Contribution to APCTP-Nankai Joint Symposium on "Lattice Statistics and Mathematical Physics", Tianjin, China,

Scientific paper

10.1142/S0217979202011846

In this report, we study the algebraic geometry aspect of Hofstadter type models through the algebraic Bethe equation. In the diagonalization problem of certain Hofstadter type Hamiltonians, the Bethe equation is constructed by using the Baxter vectors on a high genus spectral curve. When the spectral variables lie on rational curves, we obtain the complete and explicit solutions of the polynomial Bethe equation; the relation with the Bethe ansatz of polynomial roots is discussed. Certain algebraic geometry properties of Bethe equation on the high genus algebraic curves are discussed in cooperation with the consideration of the physical model.

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