Non local Thirring model with backward and umklapp interactions

TL;DR

This paper extends the non local Thirring model to include backward and umklapp interactions, deriving an effective bosonic action and gap expression for charge-density excitations in many-body systems.

Contribution

It introduces a non local, non covariant Thirring model with backward and umklapp scattering, providing a bosonic representation and a gap formula for collective excitations.

Findings

Derived a bosonic representation of the fermionic determinant.

Obtained an expression for the charge-density gap as a functional of electron-electron potentials.

Analyzed a non contact umklapp interaction case.

Abstract

We extend a non local and non covariant version of the Thirring model in order to describe a many-body system with backward and umklapp scattering processes. We express the vacuum to vacuum functional in terms of a non trivial fermionic determinant. Using path-integral methods we find a bosonic representation for this determinant which allows us to obtain an effective action for the collective excitations of the system. By introducing a non local version of the self-consistent harmonic approximation, we get an expression for the gap of the charge-density excitations as functional of arbitrary electron-electron potentials. As an example we also consider the case of a non contact umklapp interaction.