Lattice electrons in constant magnetic field: Bethe like ansatz

TL;DR

This paper develops a new explicit spectral equation for lattice electrons in a constant magnetic field using the Heisenberg-Weyl group, involving theta functions, advancing understanding of quantum lattice models.

Contribution

It introduces a Bethe-like ansatz for the model's spectrum, providing a more explicit and complex spectral equation than traditional Bethe ansatz methods.

Findings

Derived an explicit spectral equation involving theta functions.

Extended the Bethe ansatz framework to lattice electrons in magnetic fields.

Provided a new approach to analyze quantum lattice models with magnetic flux.

Abstract

We use the functional representation of Heisenberg-Weyl group and obtain equation for the spectrum of the model, which is more complicated than Bethes ones, but can be written explicitly through theta functions.