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Physical Review B

Spin transport in antiferromagnets in one and two dimensions calculated using the Kubo formula

Antonio S. T. Pires, L.S. Lima

Published Feb 4, 2009• 57 citations
Publisher

Abstract

We study spin transport in one- and two-dimensional Heisenberg antiferromagnets. In one dimension we take spin $S=1$. The longitudinal spin conductivity is calculated using the Kubo formula. The magnetic properties of low-dimensional systems are significantly modified by strong correlations effects. The models studied here show unconventional transport behavior: the computed spin conductivity exhibits a nonzero Drude weight at finite temperatures and thus a ballistic character. We present results for the regular part of the conductivity as a function of the frequency.

DOI
10.1103/physrevb.79.064401

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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.
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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.
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