arXiv:cond-mat/0410192 · Journal of the Physical Society of Japan

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Kazumitsu Sakai, Andreas Klümper

Published Jan 1, 2005• 22 citations

Abstract

Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg chain.The energy current is related to one of the non-trivial conserved quantities underlying integrability and therefore both the diagonal and off diagonal dynamical correlations of spin and energy current diverge.The energy-energy and spin-energy current correlations at finite temperatures are exactly calculated by a lattice path integral formulation.The low-temperature behavior of the thermomagnetic (magnetic Seebeck) coefficient is also discussed.Due to effects of strong correlations, we observe the magnetic Seebeck coefficient changes sign at certain interaction strengths and magnetic fields.

DOI: 10.1143/jpsjs.74s.196

Related papers

Spin and magnetothermal transport in the S = 1/2 XXZ chain

Christina Psaroudaki, X Zotos

Abstract We present a temperature and magnetic field dependence study of spin transport and magnetothermal corrections to the thermal conductivity in the spin S = 1/2 easy-plane Heisenberg chain, extending an earlier analysis based on the Bethe ansatz method. We critically discuss the low temperature, weak magnetic field behavior, the effect of magnetothermal corrections in the vicinity of the critical field and their role in recent thermal conductivity experiments in 1D quantum magnets.

arXiv:1502.05557Journal of Statistical Mechanics Theory and ExperimentJun 1, 201621 citations

Diverging magnetothermal response in the one-dimensional Heisenberg chain

Kim Louis, Claudius Gros

arXiv:cond-mat/0212161Physical review. B, Condensed matterJun 12, 200340 citations

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Shunsuke Furukawa, Dai Ikeda, Kazumitsu Sakai

arXiv:cond-mat/0508374Journal of the Physical Society of JapanDec 1, 200534 citations

Thermal transport of the XXZ chain in a magnetic field

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

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

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

Peter Jung, R. W. Helmes, Achim Rosch

arXiv:cond-mat/0509615Physical Review LettersFeb 14, 2006123 citations

Density dynamics in translationally invariant spin- 12 chains at high temperatures: A current-autocorrelation approach to finite time and length scales

Robin Steinigeweg, Jochen Gemmer B

arXiv:0906.4457Physical Review BNov 2, 200968 citations

arXiv:cond-mat/0410192 · Journal of the Physical Society of Japan

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Kazumitsu Sakai, Andreas Klümper

Published Jan 1, 2005• 22 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsjs.74s.196

Related papers

Spin and magnetothermal transport in the S = 1/2 XXZ chain

Christina Psaroudaki, X Zotos

arXiv:1502.05557Journal of Statistical Mechanics Theory and ExperimentJun 1, 201621 citations

Diverging magnetothermal response in the one-dimensional Heisenberg chain

Kim Louis, Claudius Gros

A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field B and a temperature gradient $\ensuremath{\Delta}T$ along the chain. We show that this magnetothermal effect is strictly infinite for the integrable Heisenberg model in one dimension. We set up the response formalism and derive several new generalized Einstein relations for this magnetothermal effect which vanishes in the absence of an external magnetic field. We estimate the size of the magnetothermal response by exact diagonalization and quantum Monte Carlo simulations and make contact with recent transport measurements for the one-dimensional Heisenberg compound ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$ A current of magnetic moments will flow in the spin-1/2 Heisenberg chain in the presence of an external magnetic field B and a temperature gradient $\ensuremath{\Delta}T$ along the chain. We show that this magnetothermal effect is strictly infinite for the integrable Heisenberg model in one dimension. We set up the response formalism and derive several new generalized Einstein relations for this magnetothermal effect which vanishes in the absence of an external magnetic field. We estimate the size of the magnetothermal response by exact diagonalization and quantum Monte Carlo simulations and make contact with recent transport measurements for the one-dimensional Heisenberg compound ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$

arXiv:cond-mat/0212161Physical review. B, Condensed matterJun 12, 200340 citations

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Shunsuke Furukawa, Dai Ikeda, Kazumitsu Sakai

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.

arXiv:cond-mat/0508374Journal of the Physical Society of JapanDec 1, 200534 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

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

Peter Jung, R. W. Helmes, Achim Rosch

The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin- $1/2$ nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-$1/2$ nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.

arXiv:cond-mat/0509615Physical Review LettersFeb 14, 2006123 citations

Density dynamics in translationally invariant spin- 12 chains at high temperatures: A current-autocorrelation approach to finite time and length scales

Robin Steinigeweg, Jochen Gemmer B

We investigate transport in several translationally invariant spin- $\frac{1}{2}$ chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.We investigate transport in several translationally invariant spin-$\frac{1}{2}$ chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.

arXiv:0906.4457Physical Review BNov 2, 200968 citations

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.

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.

The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-

1/2

nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength ${J}_{\ensuremath{\perp}}$ leads to $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}_{\ensuremath{\perp}}^{2}$ as expected from simple golden-rule arguments, we obtain a much larger $\ensuremath{\kappa}(T)\ensuremath{\propto}1/{J}^{\ensuremath{'}4}$ for a weak next-nearest-neighbor interaction ${J}^{\ensuremath{'}}$. This can be explained by a new approximate conservation law of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ Heisenberg chain.

We investigate transport in several translationally invariant spin-

\frac{1}{2}

chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.