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.

10 pages

References in corpus (4)

• Diffusion and ballistic transport in one-dimensional quantum systems
• Finite Drude weight for 1D low temperature conductors
• Universal Relations for Non Solvable Statistical Models
• Universality relations in non-solvable quantum spin chains

Cited by in corpus (9)

• Correlation Energy of a Weakly Interacting Fermi Gas
• Non-integrable dimers: Universal fluctuations of tilted height profiles
• Haldane relation for interacting dimers
• Universal edge transport in interacting Hall systems
• Canonical Drude weight for non-integrable quantum spin chains
• Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems
• Non-integrable dimer models: universality and scaling relations
• Weakly non-planar dimers
• The scaling limit of boundary spin correlations in non-integrable Ising models