We revisit the problem of the spin Drude weight $D$ of the integrable spin- $1/2$ XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of $D$ . By exploiting time translation invariance within tDMRG, one can extract $D$ for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.We revisit the problem of the spin Drude weight $D$ of the integrable spin-$1/2$ XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of $D$. By exploiting time translation invariance within tDMRG, one can extract $D$ for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

arXiv:1301.6401Physical Review BJun 26, 201369 citations

Thermal transport of the XXZ chain in a magnetic field

Fabian Heidrich‐Meisner, A. Honecker, W. Brenig

We study the heat conduction of the spin- $1∕2$ $XXZ$ 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.We study the heat conduction of the spin-$1∕2$ $XXZ$ 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.

arXiv:cond-mat/0408529Physical Review BMay 26, 200566 citations

Spin Drude weight of the 1D anisotropic Heisenberg spin-1/2 chain

Andrew Urichuk, Jesko Sirker, Andreas Klümper

Bulletin of the American Physical SocietyJun 2, 20210 citations

Exact results for nonlinear Drude weights in the spin- 12 XXZ chain

Yuhi Tanikawa, Kazuaki Takasan, Hosho Katsura

While the linear Drude weight in quantum many-body systems has been studied extensively, its nonlinear counterparts -- called nonlinear Drude weights (NLDWs) -- remain largely unexplored. Here, the authors present the first exact results for the NLDWs of the spin- $\frac{1}{2}$ XXZ chain, a paradigmatic quantum many-body system. Their exact results based on the Bethe ansatz reveal that the NLDWs diverge with the system size in certain parameter regions. Also, the analytical expressions for the NLDWs are obtained when they converge.While the linear Drude weight in quantum many-body systems has been studied extensively, its nonlinear counterparts -- called nonlinear Drude weights (NLDWs) -- remain largely unexplored. Here, the authors present the first exact results for the NLDWs of the spin-$\frac{1}{2}$ XXZ chain, a paradigmatic quantum many-body system. Their exact results based on the Bethe ansatz reveal that the NLDWs diverge with the system size in certain parameter regions. Also, the analytical expressions for the NLDWs are obtained when they converge.

arXiv:2103.05838Physical review. B./Physical review. BMay 27, 202115 citations

Drude Weight in Non Solvable Quantum Spin Chains

G. Benfatto, V. Mastropietro

arXiv:1012.0403Journal of Statistical PhysicsMar 25, 201113 citations

We revisit the problem of the spin Drude weight

D

of the integrable spin-

1/2

XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of

D

. By exploiting time translation invariance within tDMRG, one can extract

D

for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

We study the heat conduction of the spin-

1∕2

XXZ

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.

\frac{1}{2}

XXZ chain, a paradigmatic quantum many-body system. Their exact results based on the Bethe ansatz reveal that the NLDWs diverge with the system size in certain parameter regions. Also, the analytical expressions for the NLDWs are obtained when they converge.