An extended q-deformed su(2) algebra and the Bloch electron problem

Abstract

It is shown that an extended q-deformed $su(2)$ algebra with an extra (``Schwinger '') term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q-deformed algebra, we obtain functional Bethe ansatz equations whose solutions should be functions of finite degree. It is also shown that the zero energy solution is expressed in terms of an Askey Wilson polynomial.

11 pages, Latex

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Cited by in corpus (4)

• Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase
• The quantum algebra $U_q(s{l}_2)$ and its equitable presentation
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Augmented down-up algebras and uniform posets