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

TL;DR

This paper provides an exact finite-size analysis of the spin Drude weight in the critical spin-1/2 XXZ chain at finite temperatures, revealing slow convergence and size dependence that clarify discrepancies in previous numerical results.

Contribution

It combines thermodynamic Bethe ansatz with Y-system functional relations to evaluate the finite-size behavior of the spin Drude weight.

Findings

Drude weight converges to known results with slow finite-size convergence

Strong size dependence explains conflicting numerical extrapolations

Method provides exact finite-temperature, finite-size analysis

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.