Landau Levels from the Bethe Ansatz Equations

TL;DR

This paper derives Landau levels for 2D Bloch electrons in a magnetic field by analyzing Bethe ansatz equations in the weak field limit, providing a novel approach to understanding their energy spectrum.

Contribution

It introduces a method to calculate Landau levels from Bethe ansatz equations, linking finite size corrections to energy spectra in lattice models.

Findings

Calculated energies near the spectrum's lower boundary

Derived Landau levels from Bethe ansatz equations

Connected finite size corrections to Landau level formation

Abstract

The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.