The spin Drude weight of the spin-1/2 $XXZ$ chain: An analytic finite size study

Abstract

The Drude weight for the spin transport of the spin-1/2 $XXZ$ Heisenberg chain in the critical regime is evaluated exactly for finite temperatures. We combine the thermodynamic Bethe ansatz with the functional relations of type $Y$-system satisfied by the row-to-row transfer matrices. This makes it possible to evaluate the asymptotic behavior of the finite temperature spin Drude weight with respect to the system size. As a result, the Drude weight converges to the results obtained by Zotos (Phys. Rev. Lett. 82, 1764 (1999)), however with very slow convergence upon increase of the system size. This strong size dependence may explain that extrapolations from various numerical approaches yield conflicting results.

16 pages, Submission to SciPost

References in corpus (5)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain
• Finite Drude weight for 1D low temperature conductors

Cited by in corpus (3)

• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Spin Drude weight for the integrable XXZ chain with arbitrary spin
• Dressed excitations, thermodynamics and relaxation in the 1D XXZ Heisenberg model