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arXiv:2104.03266 · Physical review. B./Physical review. B

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

Andrew Urichuk, Jesko Sirker, Andreas Klümper

Published Jun 3, 2021• 8 citations
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Abstract

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.

DOI
10.1103/physrevb.103.245108

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We study the heat conduction of the spin-1∕21∕21∕2 XXZXXZXXZ chain in finite magnetic fields where magnetothermal effects arise. Due to the integrability of this model, all transport coefficients diverge, signaled by finite Drude weights. Using exact diagonalization and mean-field theory, we analyze the temperature and field dependence of the thermal Drude weight for various exchange anisotropies under the condition of zero magnetization-current flow. First, we find a strong magnetic field dependence of the Drude weight, including a suppression of its magnitude with increasing field strength and a nonmonotonic field-dependence of the peak position. Second, for small exchange anisotropies and magnetic fields in the massless as well as in the fully polarized regime, the mean-field approach is in excellent agreement with the exact diagonalization data. Third, at the field-induced quantum critical line between the para- and ferromagnetic region, we propose a universal low-temperature behavior of the thermal Drude weight.