Non-integrable fermionic chains near criticality

TL;DR

This paper investigates the transport properties and critical exponents of non-integrable fermionic chains near criticality, revealing that integrability does not affect these properties even when irrelevant terms dominate.

Contribution

It provides a rigorous analysis of non-integrable fermionic chains near criticality, showing no difference in exponents and conductivity compared to integrable models.

Findings

Drude weight and critical exponents computed as functions of density.

No difference between integrable and non-integrable models in exponents and conductivity.

Results based on a rigorous multiscale analysis and a partially solvable model.

Abstract

We compute the Drude weight and the critical exponents as functions of the density in non-integrable generalizations of XXZ or Hubbard chains, in the critical zero temperature regime where Luttinger liquid description breaks down and Bethe ansatz cannot be used. Even in the regions where irrelevant terms dominate, no difference between integrable and non integrable models appear in exponents and conductivity. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.