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Diverging thermal conductivity of spin-chains and ladders

Jose Vicente Alvarez, Claudius Gros

Published Jan 17, 2002• 0 citations
OpenAlex

Abstract

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 non-diverging 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.

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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 non-diverging 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 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 study the spin and thermal conductivity of spin-12\frac{1}{2}21​ ladders and chains at finite temperature, relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-12\frac{1}{2}21​ XXZXXZXXZ chains, for which our analysis suggests nonzero dc conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XXXXXX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of $T\ensuremath{\sim}0.5J$, where JJJ is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets.
The anomalous thermal conductivity in spin chains observed in experiments is studied for the low-temperature regime. In the effective dynamics with most realistic perturbations, the so-called umklapp terms are irrelevant to reduce the mean free path in the energy transport at even finite temperatures. This is consistent with the large conductivities found in recent experiments. The Drude weight which is the prefactor in the divergent conductivity is calculated, and the temperature dependence is discussed.
Motivated by recent investigations of transport properties of strongly correlated 1D models and thermal conductivity measurements of quasi 1D magnetic systems, we present results for the integrable spin-½ XXZ chain. The thermal conductivity κ(ω) of this model has ℜ κ(ω) = δ(ω), i.e. it is infinite for zero frequency ω. The weight of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low- and high-temperature limits are studied analytically.
Based on numerical simulations, a study of the high temperature, finite frequency, thermal conductivity kappa(omega) of spin-1/2 ladders is presented. The exact diagonalization and a novel Lanczos technique are employed. The conductivity spectra, analyzed as a function of rung coupling, point to a nondiverging dc limit but to an unconventional low frequency behavior. The results are discussed in perspective with recent experiments indicating a significant magnetic contribution to the energy transport in quasi-one-dimensional compounds.
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.