Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice

TL;DR

This paper explores the spectral properties of the Hofstadter problem on a hexagonal lattice, establishing duality relations and deriving Bethe-ansatz equations to analyze its quantum behavior.

Contribution

It introduces a novel duality relation between hexagonal and triangular lattices and derives Bethe-ansatz equations for the Hofstadter problem on these lattices.

Findings

Spectral relation between hexagonal and triangular lattices.

Bethe-ansatz equations for the Hofstadter system.

Insight into quantum duality in lattice systems.

Abstract

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.