arXiv:cond-mat/0204320 · Physical review. B, Condensed matter

Conductivity of quantum spin chains: A quantum Monte Carlo approach

Jose Vicente Alvarez, Claudius Gros

Published Sep 4, 2002• 30 citations

Abstract

We discuss zero-frequency transport properties of various spin-1/2 chains. We show that a careful analysis of quantum Monte Carlo data on the imaginary axis allows to distinguish between intrinsic ballistic and diffusive transport. We determine the Drude weight, current-relaxation lifetime, and the mean free path for integrable and nonintegrable quantum spin chains. We discuss, in addition, some phenomenological relations between various transport-coefficients and thermal response functions.

DOI: 10.1103/physrevb.66.094403

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arXiv:cond-mat/0204320 · Physical review. B, Condensed matter

Conductivity of quantum spin chains: A quantum Monte Carlo approach

Jose Vicente Alvarez, Claudius Gros

Published Sep 4, 2002• 30 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.66.094403

Related papers

Spin and thermal conductivity of quantum spin chains and ladders

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We study the spin and thermal conductivity of spin-

\frac{1}{2}

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-

\frac{1}{2}

XXZ

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

XX

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

J

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.

We report a detailed analysis of the Drude weights for both thermal and spin transport in one-dimensional spin-

\frac{1}{2}

systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable

\mathrm{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 investigate energy transport in several two-level atom or spin-

1∕2

models by a direct coupling to heat baths of different temperatures. The analysis is carried out on the basis of a recently derived quantum master equation which describes the nonequilibrium properties of internally weakly coupled systems appropriately. For the computation of the stationary state of the dynamical equations, we employ a Monte Carlo wave-function approach. The analysis directly indicates normal diffusive or ballistic transport in finite models and hints toward an extrapolation of the transport behavior of infinite models.