Magnetic translation symmetry on the lattice

TL;DR

This paper explores magnetic translation symmetry on finite periodic lattices under uniform magnetic fields, providing a classification method for eigenvectors, dimensional reduction techniques, and a higher-dimensional Harper equation generalization.

Contribution

It introduces a comprehensive analysis of magnetic translation symmetry, including classification of eigenvectors, dimensional reduction, and a higher-dimensional Harper equation extension.

Findings

Eigenvector classification using magnetic translation symmetry

Dimensional reduction of lattice systems

Generalization of Harper equation to higher dimensions

Abstract

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to another system of half or lower dimensions. A higher dimensional generalization of Harper equation is obtained for tight-binding systems.