Bosonization on the lattice: the emergence of the higher harmonics

TL;DR

This paper introduces a clear lattice bosonization method revealing higher harmonics in the Green function caused by electron band compactness, enabling quantitative analysis of these effects.

Contribution

It presents a novel bosonization procedure for lattice fermions that explicitly accounts for higher harmonics in the Green function.

Findings

Higher harmonics appear due to band compactness.

Quantitative estimations of higher harmonic effects are possible.

The method enhances understanding of lattice fermion behavior.

Abstract

A general and transparent procedure to bosonize fermions placed on a lattice is presented. Harmonics higher than $k_F$ are shown to appear in the one-paticle Green function, due to the compact character of real electron bands. Quantitative estimations of the role of these higher harmonics are made possible by the bosonization technique presented here.