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arXiv:cond-mat/0302358 · Physical Review Letters

Comment on “Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders”

Fabian Heidrich‐Meisner, A. Honecker, D. C. Cabra, W. Brenig

Published Feb 11, 2004• 33 citations
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Abstract

In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.

DOI
10.1103/physrevlett.92.069703

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In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.
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 study the thermal transport properties of several quantum-spin chains and ladders. We find indications for a diverging thermal conductivity at finite temperatures for the models examined. The temperature at which the nondiverging prefactor kappa((th))(T) peaks is, in general, substantially lower than the temperature at which the corresponding specific heat c(V)(T) is maximal. We show that this result of the microscopic approach leads to a substantial reduction for estimates of the magnetic mean-free path lambda extracted by analyzing recent experiments, as compared to similar analyses by phenomenological theories.
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.
The spin Drude weight of the spin-1/2 XXZXXZXXZ chain: An analytic finite size study
The Drude weight for the spin transport of the spin-1/2 XXZXXZXXZ Heisenberg chain in the critical regime is evaluated exactly for finite temperatures. We combine the thermodynamic Bethe ansatz with the functional relations of type YYY-system satisfied by the row-to-row transfer matrices. This makes it possible to evaluate the asymptotic behavior of the finite temperature spin Drude weight with respect to the system size. As a result, the Drude weight converges to the results obtained by Zotos (Phys. Rev. Lett. 82, 1764 (1999)), however with very slow convergence upon increase of the system size. This strong size dependence may explain that extrapolations from various numerical approaches yield conflicting results.
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We analyze the thermal conductivity of anisotropic and frustrated spin-1/2 chains using analytical and numerical techniques. This includes mean-field theory based on the Jordan-Wigner transformation, bosonization, and exact diagonalization of systems with N< 18N<~18N< 18 sites. We present results for the temperature dependence of the zero-frequency weight of the conductivity for several values of the anisotropy \ensuremath{\Delta}. In the gapless regime, we show that the mean-field theory compares well to known results and that the low-temperature limit is correctly described by bosonization. In the antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature dependence of the thermal conductivity numerically. The convergence of the finite-size data is remarkably good in the ferromagnetic case. Finally, we apply our numerical method and mean-field theory to the frustrated chain where we find a good agreement of these two approaches on finite systems. Our numerical data do not yield evidence for a diverging thermal conductivity in the thermodynamic limit in case of the antiferromagnetic gapped regime of the frustrated chain.