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arXiv:cond-mat/0605405

Issues on the transport of one dimensional systems

X. Zotos

Published May 16, 2006• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.cond-mat/0605405

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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.
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.
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.
The author’s book [1] on quantum phase transitions has an extensive discussion on the dynamic and transport properties of a variety of systems at non-zero temperatures above a zero temperature quantum critical point. The purpose of this chapter is to briefly review some basic material, and to then update the earlier discussion with a focus on experimental and theoretical developments in the decade since the book was written. We note other recent reviews [2] from which portions of this chapter have been adapted.
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.
Abstract For a number of quantum critical points in one dimension quantum field theory has provided exact results for the scaling of spatial and temporal correlation functions. Experimental realizations of these models can be found in certain quasi one dimensional antiferromagnetic materials. Measuring the predicted scaling laws experimentally presents formidable technical challenges. In many cases it only became possible recently, thanks to qualitative progress in the development of inelastic neutron scattering techniques and to the discovery of new model compounds. Here we review some of the recent experimental studies of this type.