G. Benfatto, V. Mastropietro
Drude weight in non solvable quantum spin chains
(678K, Postscript)

ABSTRACT.  For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation $v_s^2=D/\k$, where $\k$ is the susceptibility and $v_s$ is the Fermi velocity. This result is proved by rigorous Renormalization Group methods and is true for any weakly interacting system, regardless its integrablity. This paper, combined with a previous one of the authors, completes the proof of the Luttinger liquid conjecture for such systems.