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arXiv:cond-mat/0105585 · Physical Review Letters

Low-Temperature Transport in Heisenberg Chains

Jose Vicente Alvarez, Claudius Gros

Published Feb 1, 2002• 91 citations
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Abstract

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.

DOI
10.1103/physrevlett.88.077203

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We propose an easily implemented approach to study time-dependent correlation functions of one-dimensional systems at finite-temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long-time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero--and thus transport is dissipationless--everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.