Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Bloch Electrons in a Magnetic Field
P.B Wiegmann, A.V.Zabrodin
TL;DR
This paper introduces a novel method linking magnetic translations to quantum groups, enabling the spectrum and Bloch functions of electrons in magnetic fields to be solved via Bethe-Ansatz equations, advancing understanding of integrable quantum systems.
Contribution
It establishes a direct relation between magnetic translations and quantum groups, providing a new framework for solving Bloch electron problems in magnetic fields.
Findings
Spectrum expressed through Bethe-Ansatz equations.
Bloch functions derived from integrable quantum system solutions.
New connection between magnetic translations and quantum groups.
Abstract
We present a new approach to the problem of Bloch electrons in magnetic field,\\ by making explicit a natural relation between magnetic translations and the\\quantum group . The approach allows to express the spectrum and\\\ the Bloch function as solutions of the Bethe-Ansatz equations typical for com\\pletely integrable quantum systems
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