Hofstadter problem on the honeycomb and triangular lattices: Bethe ansatz solution

2006/03/10 by Mahito Kohmoto, M. Kohmoto, A. Sedrakyan · 2 citations
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Finite Group Theory Research #Matrix Theory and Algorithms #Quasicrystal Structures and Properties #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.73.235118

published as Phys. Rev. B 73, 235118 (2006) · 7 pages, 2 figures, Revtex

arxiv created 2006/03/10 · openalex publication_date 2006/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with 2\ensuremathπp∕q flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as a 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 us to consider them further in the limit p,q\ensuremath→\ensuremath∞ by the technique of thermodynamic Bethe ansatz and analyze the Hofstadter problem for the irrational flux.

Citations

• Magnetic Translation Group

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