Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

Details Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

1995-09-12

arxiv.org/abs/cond-mat/9509062v1

Physics

Condensed Matter

30 pages, 11 GIF figures(use xv, or WWW browser)

Scientific paper

10.1103/PhysRevB.53.9697

The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $\phi=1/Q$ is analyzed in detail, by exploring a structure of the Bethe Ansatz equations. We also reveal the multifractal structure of the Bethe Ansatz solutions and corresponding wave functions when $\phi$ is irrational, such as the golden or silver mean.

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