Confinement and quantum anomaly in quasi-1D spinless fermion chains

TL;DR

This paper studies the renormalization group flow of coupled 1D spinless fermion chains, revealing quantum confinement and anomalies, and showing the system's equivalence to multi-color interactions with Luttinger liquid fixed points.

Contribution

It demonstrates quantum confinement and anomalies in coupled 1D fermion chains using two-loop RG analysis, providing a novel understanding of their fixed points and effective descriptions.

Findings

Quantum confinement reduces interband Fermi points to single points.

Renormalized couplings exhibit Luttinger liquid fixed points.

Quantum anomaly arises from coupling Dirac fields to multi-color interactions.

Abstract

We consider the field renormalization group (RG) of two coupled one-spatial dimension (1D) spinless fermion chains under intraforward, interforward, interbackscattering and interumklapp interactions until two-loops order. Up to this order, we demonstrate the quantum confinement in the RG flow, where the interband chiral Fermi points reduce to single chiral Fermi points and the renormalized interaction couplings have Luttinger liquid fixed points. We show that this quasi-1D system is equivalently described in terms of one and two-color interactions and address the problem of quantum anomaly, inherent to this system, as a direct consequence of coupling 1+1 free Dirac fields to one and two-color interactions.