Precise Wigner-Weyl calculus for lattice models

TL;DR

This paper introduces a novel Wigner-Weyl calculus tailored for lattice models, enabling the expression of physical quantities like Hall conductivity as topological invariants even under strong magnetic fields.

Contribution

A new Wigner-Weyl calculus for lattice models that expresses physical quantities as topological invariants, applicable to strong magnetic fields.

Findings

Hall conductivity represented as a topological invariant

Formalism applicable to varying and strong magnetic fields

Provides a new computational framework for lattice models

Abstract

We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Green's functions. In particular, Hall conductivity in the presence of varying and arbitrarily strong magnetic field is represented using the proposed formalism as a topological invariant.