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

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

2006-03-10

arxiv.org/abs/cond-mat/0603285v1

Phys. Rev. B 73, 235118 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, 2 figures, Revtex

Scientific paper

10.1103/PhysRevB.73.235118

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 \pi p/q$ 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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