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arXiv:cond-mat/0301253 · Physical Review Letters

Drude Weight at Finite Temperatures for Some Nonintegrable Quantum Systems in One Dimension

Satoshi Fujimoto, Norio Kawakami

Published May 15, 2003• 61 citations
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Abstract

Using conformal perturbation theory, we show that, for some classes of the one-dimensional quantum liquids that possess the Luttinger liquid fixed point in the low-energy limit, the Drude weight at finite temperatures is nonvanishing, even when the system is nonintegrable and the total current is not conserved. We also obtain the asymptotically exact low-temperature formula of the Drude weight for Heisenberg XXZ spin chains, which agrees quite well with recent numerical data.

DOI
10.1103/physrevlett.90.197202

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Using conformal perturbation theory, we show that, for some classes of the one-dimensional quantum liquids that possess the Luttinger liquid fixed point in the low-energy limit, the Drude weight at finite temperatures is nonvanishing, even when the system is nonintegrable and the total current is not conserved. We also obtain the asymptotically exact low-temperature formula of the Drude weight for Heisenberg XXZ spin chains, which agrees quite well with recent numerical data.
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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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A technique to determine accurately transport properties of integrable and nonintegrable quantum-spin chains at finite temperatures by quantum Monte Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of Drude weight in the gapless regime of a nonintegrable system with longer-ranged interactions is presented. We estimate the effect of the nonintegrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.
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