Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids

TL;DR

This paper demonstrates the first example of asymptotic Spin-Charge separation in a non-solvable one-dimensional fermionic model using Renormalization Group techniques, extending understanding beyond traditional solvable systems.

Contribution

It introduces a novel application of Renormalization Group combined with Ward-Identities and Schwinger-Dyson equations to analyze Spin-Charge separation in non-solvable models.

Findings

First example of asymptotic Spin-Charge separation in a non-solvable 1D model

Application of RG, Ward-Identities, and Schwinger-Dyson equations to non-solvable systems

Methods potentially applicable to lattice and higher-dimensional systems

Abstract

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d=1 non solvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems.