Competition of Phonons and Magnetic Interaction in One-Dimensional Fermion Systems

TL;DR

This paper investigates the competition between phonon-induced effects and magnetic interactions in one-dimensional fermion systems, revealing complex interplay and fixed points through renormalization group analysis.

Contribution

It introduces a renormalization group approach to analyze the competition between phonon effects and magnetic interactions in 1D fermion systems.

Findings

Non-interacting fermions form a semi-stable fixed point.

Phonons induce Peierls instability or long-range correlations.

Competition leads to a third interaction in the system.

Abstract

We consider a system of spin-dependent fermions on a one-dimensional lattice which is coupled to phonons. The phonons create either a Peierls instability by breaking the translational invariance or create long range correlations. On the other hand, there is a spin-dependent Hubbard-like interaction which competes with the effective fermion-fermion interaction induced by the phonons. We investigate the competition of both interactions using a renormalization group calculation for weak interaction. The renormalization group transformation creates a third interaction. It turns out that non-interacting fermions represent a semi-stable fixed point of the fermion system.