Canonical Drude weight for non-integrable quantum spin chains

Abstract

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably the proof works for both for integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.

Two appendices added, minor corrections. 18 pages

References in corpus (6)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Propagation of Correlations in Quantum Lattice Systems
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Non perturbative Adler-Bardeen Theorem
• The scaling limit of the energy correlations in non integrable Ising models
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

Cited by in corpus (6)

• Super-diffusion in one-dimensional quantum lattice models
• Quantization of the interacting Hall conductivity in the critical regime
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure
• Anomaly non-renormalization in interacting Weyl semimetals
• Non-integrable fermionic chains near criticality