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arXiv:cond-mat/0211633 · Physical review. B, Condensed matter

Thermal transport in one-dimensional spin gap systems

E. Orignac, R. Chitra, R. Citro

Published Apr 28, 2003• 69 citations
arXivHTMLPDF

Abstract

We study thermal transport in one-dimensional spin systems both in the presence and absence of impurities. In the absence of disorder, all these spin systems display in the continuum limit a temperature-dependent Drude peak in the thermal conductivity. In gapless systems, the low-temperature Drude weight is proportional to temperature and to the central charge, which characterizes the conformal field theory that describes the system at low energies. On the other hand, the low-temperature Drude weight of spin gap systems shows an activated behavior modulated by a power law. For temperatures higher than the spin gap, one recovers the linear T behavior akin to gapless systems. For temperatures larger than the exchange coupling, the Drude weight decays as ${T}^{\ensuremath{-}2}.$ We argue that this behavior is a generic feature of quasi-one-dimensional spin gap systems with a relativistic like low-energy dispersion. We also consider the effect of a magnetic field on the Drude weight with emphasis on the commensurate-incommensurate transition induced by it. We then study the effect of nonmagnetic impurities on the thermal conductivity of the dimerized $\mathrm{XY}$ chain and the spin-$\frac{1}{2}$ two-leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.

DOI
10.1103/physrevb.67.134426

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We study thermal transport in one-dimensional spin systems both in the presence and absence of impurities. In the absence of disorder, all these spin systems display in the continuum limit a temperature-dependent Drude peak in the thermal conductivity. In gapless systems, the low-temperature Drude weight is proportional to temperature and to the central charge, which characterizes the conformal field theory that describes the system at low energies. On the other hand, the low-temperature Drude weight of spin gap systems shows an activated behavior modulated by a power law. For temperatures higher than the spin gap, one recovers the linear T behavior akin to gapless systems. For temperatures larger than the exchange coupling, the Drude weight decays as T\ensuremath−2.{T}^{\ensuremath{-}2}.T\ensuremath−2. We argue that this behavior is a generic feature of quasi-one-dimensional spin gap systems with a relativistic like low-energy dispersion. We also consider the effect of a magnetic field on the Drude weight with emphasis on the commensurate-incommensurate transition induced by it. We then study the effect of nonmagnetic impurities on the thermal conductivity of the dimerized XY\mathrm{XY}XY chain and the spin-12\frac{1}{2}21​ two-leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.
This thesis studies transport properties of low-dimensional quantum spin systems with a particular focus on the transport of heat and spin. While the integrable anisotropic spin-1/2 chain exhibits ballistic transport (finite Drude weights), the numerical results of this work show that heat and spin transport of non-integrable models (spin ladder, frustrated and dimerized chain) is not ballistic, characterized by vanishing Drude weights in the thermodynamic limit. The results for the thermal conductivity of spin ladders are compared to experimental data. For the case of the spin-1/2 Heisenberg chain, this work contains detailed results for the temperature and magnetic field dependence of the Drude weights. Finally, bond-disordered spin systems are considered, namely the spin-1/2 chain and the spin ladder. In the first case, the transport coefficients are computed by means of exact diagonalization and discussed as a function of frequency, temperature, and magnetic field. In the second case, spectral properties of the elementary excitation of disordered spin ladders are analyzed using diagrammatic perturbation theory and numerical techniques.
We report a detailed analysis of the Drude weights for both thermal and spin transport in one-dimensional spin-12\frac{1}{2}21​ systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable XXZ\mathrm{XXZ}XXZ model and second for various nonintegrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with those of the Bethe ansatz, bosonization, and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the nonintegrable models, a finite-size analysis of the numerical data for the Drude weights is presented, covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question of whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for nonintegrable models.
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.
We study the spin and heat conductivity of dimerized spin-12\frac{1}{2}21​ chains in homogeneous magnetic fields at finite temperatures. At zero temperature, the model undergoes two field-induced quantum phase transitions from a dimerized, into a Luttinger, and finally into a fully polarized phase. We search for signatures of these transitions in the spin and heat conductivities. Using exact diagonalization, we calculate the Drude weights, the frequency dependence of the conductivities, and the corresponding integrated spectral weights. As a main result, we demonstrate that both the spin and heat conductivity are enhanced in the gapless phase and most notably at low frequencies. In the case of the thermal conductivity, however, the field-induced increase seen in the bare transport coefficients is suppressed by magnetothermal effects, caused by the coupling of the heat and spin current in finite magnetic fields. Our results complement recent magnetic transport experiments on spin-ladder materials with sufficiently small exchange couplings allowing access to the field-induced transitions.
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We present an exact theory that describes how magnetic impurities change the behavior of the thermal conductivity for the integrable Heisenberg antiferromagnetic quantum spin-1/2 chain. Single magnetic impurities and a large concentration of impurities with similar values of the couplings to the host chain (a weak disorder) do not change the linear-in-temperature low-T behavior of the thermal conductivity: Only the slope of that behavior becomes smaller, compared to the homogeneous case. The strong disorder in the distribution of the impurity-host couplings produces more rapid temperature growth of the thermal conductivity, compared to the linear-in-T dependence of the homogeneous chain and the chain with weak disorder. Recent experiments on the thermal conductivity in inhomogeneous quasi-one-dimensional quantum spin systems manifest qualitative agreement with our results.