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Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

M. Kohmoto·A. Sedrakyan
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Abstract

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 πp/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.

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M. Kohmoto, A. Sedrakyan. 2006-03-10. Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution. https://doi.org/10.1103/physrevb.73.235118

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