FM 11-2010 (arXiv:1012.0403)

Authors: Giuseppe Benfatto and Vieri Mastropietro

Title: Drude weight in non solvable quantum spin chains
 
Abstract: For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation $v_s^2=D/\kappa$, where $\kappa$ 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 paper of the same authors, completes the proof of the Luttinger liquid conjecture for such systems.

Keywords: One-dimensional lattice fermions, Luttinger liquid conjecture, Haldane's relation, universality, non-integrable systems, Renormalization Group.

Giuseppe Benfatto
Dipartimento di Matematica
Università di Roma Tor Vergata
V.le della Ricerca Scientifica 1, 00133 Roma - Italy
e-mail: benfatto AT mat DOT uniroma2 DOT it

Vieri Mastropietro
Dipartimento di Matematica
Università di Roma Tor Vergata
V.le della Ricerca Scientifica 1, 00133 Roma - Italy
e-mail: mastropi AT mat DOT uniroma2 DOT it