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arXiv:cond-mat/0212161 · Physical review. B, Condensed matter

Diverging magnetothermal response in the one-dimensional Heisenberg chain

Kim Louis, Claudius Gros

Published Jun 12, 2003• 40 citations
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Abstract

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

DOI
10.1103/physrevb.67.224410

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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 \ensuremathΔT\ensuremath{\Delta}T\ensuremathΔT 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 Sr2CuO3.{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.Sr2​CuO3​.
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.
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.
The heat conductivity $\ensuremath{\kappa}(T)$ of integrable models, like the one-dimensional spin-1/21/21/2 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 study a spin-1/2 model with triangular XXZXXZXXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate ``classical'' Ising spins. Diagonalization of the triangular XXZXXZXXZ clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization MMM equal to fractions 0, 1/41/41/4, and 1/21/21/2 of the saturation magnetization M=1M=1M=1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of T=0T=0T=0 magnetization curves, entropy as a function of temperature TTT and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.
We study thermal transport in a classical one-dimensional Heisenberg model employing a discrete-time odd-even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time step $\ensuremath{\Delta}t$. We rigorously show that in presence of driving, the system attains local thermal equilibrium, which is a strict requirement of Fourier law. In the thermodynamic limit, heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in zero- and infinite-temperature limits.