Non local Thirring model with backward and umklapp interactions

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.

19 pages, no figures

References in corpus (8)

• Renormalization Group Approach to Interacting Fermions
• Path-Integral bosonization of a non-local interaction and its application to the study of 1-d many-body systems
• Equivalent bosonic theory for the massive Thirring model with non-local interaction
• Vacuum properties of a Non-Local Thirring-Like Model
• Non-local Thirring model at finite-temperature
• Exactly Soluble Model for Umklapp Scattering at Quantum-Hall Edges
• Non local Thirring model with spin flipping interactions
• Path-integral formulation of backward and umklapp scattering for 1d spinless fermions

Cited by in corpus (3)

• RG study of a non local sine-Gordon model
• A non covariant fermionic determinant and its connection to Luttinger systems
• Current conservation in charge conjugation parity time reversal symmetry (CPT) violating gauge-invariant nonlocal Thirring model