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

TL;DR

This paper develops a field-theoretical approach to analyze non-local interactions in a 1D electron system with fermionic impurities, deriving exact collective mode dispersions and correlation functions, and exploring implications for Fermi liquid behavior.

Contribution

It introduces a path-integral non-local bosonization method applied to a Thirring-like model with impurities, providing exact solutions for collective modes and correlations.

Findings

Derived exact dispersion relations for collective modes.

Obtained explicit fermionic correlation functions.

Suggested potential mechanisms for restoring Fermi liquid behavior.

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.