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arXiv:cond-mat/0304630

Transport in one dimensional quantum systems

X. Zotos, Peter Prelovšek

Published Apr 28, 2003• 11 citations
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Abstract

In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the unconventional transport and dynamic - spin, electrical, thermal - properties implied by the integrability of models as the spin-1/2 Heisenberg chain or Hubbard. Furthermore, we address the implication of these developments to experimental studies and theoretical descriptions by low energy effective theories.

DOI
10.48550/arxiv.cond-mat/0304630

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In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the unconventional transport and dynamic - spin, electrical, thermal - properties implied by the integrability of models as the spin-1/2 Heisenberg chain or Hubbard. Furthermore, we address the implication of these developments to experimental studies and theoretical descriptions by low energy effective theories.
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In this paper, we will critically discuss recent theoretical and experimental developments on the transport of one dimensional quantum systems. In particular, we will focus on open issues and controversial results related to the finite temperature dynamics of integrable quantum models. These singular systems are commonly used in the description of quasi-one dimensional materials. They have recently attracted a lot of interest in connection to the interpretation of experiments, specially after the discovery of unusual thermal conductivity in magnetic 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.
In this thesis we present the results of calculations of the properties of quantum spin systems. \nThe majority of the work is concerned with one dimensional spin chains and the particular \neffects that reduced dimensionality produce. The final chapter describes some earlier work on \nmixed valence manganite compounds. \nWe demonstrate one derivation of the Heisenberg Hamiltonian and discuss its applicability to \nmodelling magnetic systems both in three and one dimension. We discuss systems that are \nexactly soluble and the failure of spin wave theory in I-D. The Density-Matrix \nRenormalisation Group (DMRG) method is discussed in detail as is the extension to finite \ntemperature (TMRG). \nWe show results of calculations on a number of S=1/2 and S=l models and fundamental \ndifferences in their excitation spectra is observed. The thermodynamics of these systems have \nbeen obtained over a wide temperature range. In addition, excellent agreement with \nexperiment is shown for a number of quasi one dimensional compounds. The DMRG and \nTMRG are shown to be very competitive and accurate methods of studying such systems, \nespecially in the case of gapped systems. \nThe final chapter discusses the role of correlated magnetic clusters in determining the magnetic \nproperties of mixed valence manganites at temperatures near the Curie temperature. Our \nresults are supported by recent direct experimental observation of the formation of these \nclusters. We also briefly discuss some preliminary results regarding the effect of an interface \non the electronic and magnetic properties of these compounds.
Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real materials are expected to have singular effects on transport quantities: integrable models often support dissipationless transport, while weak nonintegrable terms lead to finite conductivities. We use matrix-product-state methods to obtain quantitative values of spin/electrical and thermal conductivities in an almost integrable gapless (XXZXXZXXZ-like) spin chain. At low temperatures, we observe power laws whose exponents are solely determined by the Luttinger liquid parameter. This indicates that our results are independent of the actual model under consideration.