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arXiv:0907.2837 · Journal of Statistical Physics

Universality Relations in Non-solvable Quantum Spin Chains

G. Benfatto, V. Mastropietro

Published Jan 8, 2010• 22 citations
arXivHTMLPDF
DOI
10.1007/s10955-010-9920-0

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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 vs 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 [1], completes the proof of the Luttinger liquid conjecture for such systems. 1 Introduction and main result Quantum spin chains and one dimensional Fermi systems have been the subject of an intense theoretical investigation for decades, either for their remarkable properties or for the fact that they can be experimentally realized in systems like quantum spin chain models (KCuF3) [2] or carbon nanotubes [3]. We consider a quantum spin chain model
We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, and Haldane, but only checked in the special solvable models; one of them, related to the anisotropic Ashkin-Teller model, is novel.