Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure

TL;DR

This paper proves the universal Luttinger liquid relations for one-dimensional spinning fermion systems using Ward Identities and effective models, completing a prior work and establishing fundamental symmetry-based properties.

Contribution

It introduces an effective model with additional symmetries and relates its critical exponents to the lattice fermion gas through parameter tuning, advancing the understanding of universality in 1D Fermi systems.

Findings

Proof of universal Luttinger liquid relations for spinning fermions

Relation of critical exponents between effective model and lattice gas

Use of Ward Identities to establish symmetry-based results

Abstract

We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to asymptotically emerging symmetries. This is done by introducing an effective model verifying extra symmetries and by relating its critical exponents to those of the fermion lattice gas by suitable fine tuning of the parameters.