One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

Adilet Imambekov, Thomas L. Schmidt, and Leonid I. Glazman
Rev. Mod. Phys. 84, 1253 – Published 14 September 2012

Abstract

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.

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  • Received 6 October 2011

DOI:https://doi.org/10.1103/RevModPhys.84.1253

© 2012 American Physical Society

Authors & Affiliations

Adilet Imambekov

  • Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

Thomas L. Schmidt* and Leonid I. Glazman

  • Department of Physics, Yale University, New Haven, Connecticut 06520, USA

  • *thomas@thoschmidt.de
  • leonid.glazman@yale.edu

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Vol. 84, Iss. 3 — July - September 2012

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