For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation v^2_s = 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.
Benfatto, G., Mastropietro, V. (2011). Drude Weight in Non Solvable Quantum Spin Chains. JOURNAL OF STATISTICAL PHYSICS, 143(2), 251-260 [10.1007/s10955-011-0181-3].
Drude Weight in Non Solvable Quantum Spin Chains
BENFATTO, GIUSEPPE;MASTROPIETRO, VIERI
2011-02-01
Abstract
For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation v^2_s = 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.| File | Dimensione | Formato | |
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