Andrew Urichuk, Yahya Oez, Andreas Klümper, Jesko Sirker
SciPost Phys. 6, 005 (2019) ·
published 11 January 2019
Based on a generalized free energy we derive exact thermodynamic Bethe ansatz
formulas for the expectation value of the spin current, the spin
current-charge, charge-charge correlators, and consequently the Drude weight.
These formulas agree with recent conjectures within the generalized
hydrodynamics formalism. They follow, however, directly from a proper treatment
of the operator expression of the spin current. The result for the Drude weight
is identical to the one obtained 20 years ago based on the Kohn formula and
TBA. We numerically evaluate the Drude weight for anisotropies
$\Delta=\cos(\gamma)$ with $\gamma = n\pi/m$, $n\leq m$ integer and coprime. We
prove, furthermore, that the high-temperature asymptotics for general
$\gamma=\pi n/m$---obtained by analysis of the quantum transfer matrix
eigenvalues---agrees with the bound which has been obtained by the construction
of quasi-local charges.