Federico Bonetto, Vieri Mastropietro Non-integrable fermionic chains near criticality. (601K, pdf) ABSTRACT. We obtain 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. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.