Field theoretical approach to non-local interactions: 1d electrons and fermionic impurities

Abstract

We apply a recently proposed path-integral approach to non-local bosonization to a Thirring-like system modeling non-relativistic massless particles interacting with localized fermionic impurities. We consider forward scattering processes described by symmetric potentials including interactions between charge, current, spin and spin-current densities. In the general (spin-flipping) problem we obtain an effective action for the collective modes of the model at T = 0, containing WZW-type terms. When spin-flipping processes are disregarded the structure of the action is considerably simplified, allowing us to derive exact expressions for the dispersion relations of collective modes and two point fermionic correlation functions as functionals of the potentials. Finally, as an example, we compute the momentum distribution for the case in which electrons and impurities are coupled through spin and spin-current densities only. The formulae we get suggest that our formalism could be useful in order to seek for a mechanism able to restore Fermi liquid behavior.

27 pages, Latex file, no figures

References in corpus (3)

• One-Dimensional Fermi liquids
• Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D Electron Gas
• Path-Integral bosonization of a non-local interaction and its application to the study of 1-d many-body systems

Cited by in corpus (7)

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• Equivalent bosonic theory for the massive Thirring model with non-local interaction
• Non-local Thirring model at finite-temperature
• Vacuum properties of a Non-Local Thirring-Like Model
• Non local Thirring model with spin flipping interactions
• RG study of a non local sine-Gordon model