Drude Weight in Non Solvable Quantum Spin Chains

摘要

For a quantum spin chain or 1D fermionic system, we prove that the Drude weightD verifies the universal Luttinger liquid relation ν_s~2=D/κ, where κ 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 integrability. This paper, combined with Benfatto and Mastropietro (in J. Stat. Phys. 138, 1084-1108, 2010), completes the proof of the Luttinger liquid conjecture for such systems.