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.
Cited by 4
Jacopo De Nardis et al., Diffusion in generalized hydrodynamics and quasiparticle scattering
SciPost Phys. 6, 049 (2019) [Crossref]
Vir B. Bulchandani et al., Subdiffusive front scaling in interacting integrable models
Phys. Rev. B 99, 121410 (2019) [Crossref]
Marko Ljubotina et al., Ballistic Spin Transport in a Periodically Driven Integrable Quantum System
Phys. Rev. Lett. 122, 150605 (2019) [Crossref]
Jean-Marie Stéphan, Free fermions at the edge of interacting systems
SciPost Phys. 6, 057 (2019) [Crossref]
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- 1 Bergische Universität Wuppertal / University of Wuppertal [BUW]
- 2 Université du Manitoba / University of Manitoba