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A finite-temperature phase transition for disordered weakly interacting bosons in one dimension

Nature Physics volume 6, pages 900–904 (2010)Cite this article

Abstract

It is commonly accepted that there are no phase transitions in one-dimensional systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we show theoretically that the one-dimensional gas of short-range interacting bosons in the presence of disorder can undergo a finite-temperature phase transition between two distinct states: fluid and insulator. Neither of these states has long-range spatial correlations, but this is a true, albeit non-conventional, phase transition, because transport properties are singular at the transition point. In the fluid phase, mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. This study thus provides insight into how the interaction between disordered bosons influences their Anderson localization. This question, first raised for electrons in solids, is now crucial for the studies of atomic bosons, where recent experiments have demonstrated Anderson localization in expanding dilute quasi-one-dimensional clouds.

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Figure 1: Properties of single-particle localization.
Figure 2: Scattering processes leading to the localization–delocalization transition.
Figure 3: Phase diagram for weakly interacting disordered bosons.
Figure 4: Manifestation of the many-body localization–delocalization transition in the expansion of a quasi-1D cloud.

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Acknowledgements

We are grateful to A. Aspect and J. Dalibard for interesting discussions, and to M. Foster and L. Glazman for comments on the manuscript. We acknowledge support from US DOE Contract DE-AC02-06CH11357, from the IFRAF Institute of Ile de France and from ANR (Grant ANR-08-BLAN-0165). G.V.S. was also supported by the Dutch Foundation FOM. Part of the work was carried out during the workshop ‘From Femtoscience to Nanoscience: Nuclei, Quantum Dots, and Nanostructures’ in the Institute of Nuclear Theory at the University of Washington.

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Authors and Affiliations

  1. Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA

    I. L. Aleiner & B. L. Altshuler

  2. Laboratoire de Physique Théorique et Modèles Statistique, Université Paris Sud, CNRS, 91405 Orsay, France

    G. V. Shlyapnikov

  3. Van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65/67, 1018 XE Amsterdam, The Netherlands

    G. V. Shlyapnikov

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  1. I. L. Aleiner
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All authors contributed extensively to the work presented in this paper.

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Correspondence to I. L. Aleiner.

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Aleiner, I., Altshuler, B. & Shlyapnikov, G. A finite-temperature phase transition for disordered weakly interacting bosons in one dimension. Nature Phys 6, 900–904 (2010). https://doi.org/10.1038/nphys1758

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