Non-integrable fermionic chains near criticality

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 high- or low-density regime where the dispersion becomes almost quadratic, the Luttinger liquid description breaks down and the Bethe ansatz cannot be used. Even in the regions where irrelevant terms dominate, no difference between integrable and non-integrable models appears in exponents and conductivity at zero temperature. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.