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

Andreas Klümper, Kazumitsu Sakai

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.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.

arXiv:1904.11253Apr 25, 20194 citations

Analytical results for the low-temperature Drude weight of the XXZ spin chain

Andrew Urichuk, Jesko Sirker, Andreas Klümper

Nondecaying dc currents in systems showing ballistic transport are characterized by a constant, known as the Drude weight. Here, the authors obtain analytical results for the spin Drude weight in the interacting anisotropic Heisenberg spin- $\frac{1}{2}$ chain at low temperatures. The obtained analytical formula reveals that the Drude weight for any finite temperature exhibits a nowhere-continuous dependence on the spin anisotropy of the model.Nondecaying dc currents in systems showing ballistic transport are characterized by a constant, known as the Drude weight. Here, the authors obtain analytical results for the spin Drude weight in the interacting anisotropic Heisenberg spin-$\frac{1}{2}$ chain at low temperatures. The obtained analytical formula reveals that the Drude weight for any finite temperature exhibits a nowhere-continuous dependence on the spin anisotropy of the model.

arXiv:2104.03266Physical review. B./Physical review. BJun 3, 20218 citations

The spin Drude weight of the spin-1/2

XXZ

chain: An analytic finite size study

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.

\frac{1}{2}

chain at low temperatures. The obtained analytical formula reveals that the Drude weight for any finite temperature exhibits a nowhere-continuous dependence on the spin anisotropy of the model.