Algebraic Geometry Approach to the Bethe Equation for Hofstadter Type Models
Shao-shiung Lin, Shi-shyr Roan
TL;DR
This paper applies algebraic geometry to solve the Bethe equation for Hofstadter-type models, providing explicit solutions for rational flux cases and exploring high genus curve properties.
Contribution
It introduces an algebraic geometry framework to analyze the Bethe equation, yielding explicit solutions and insights into high genus algebraic curves in Hofstadter models.
Findings
Explicit solutions for rational magnetic flux models.
Analysis of Bethe equations on high genus algebraic curves.
Discussion of thermodynamic flux limit behavior.
Abstract
We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit solutions for models with the rational magnetic flux, and discuss the Bethe equation of their thermodynamic flux limit. The algebraic geometry properties of the Bethe equation on high genus algebraic curves are investigated in cooperation
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