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Superfluid-insulator transition of disordered bosons in one dimension

Altman, Ehud and Kafri, Yariv and Polkovnikov, Anatoli and Refael, Gil (2010) Superfluid-insulator transition of disordered bosons in one dimension. Physical Review B, 81 (17). Art. No. 174528. ISSN 0163-1829. doi:10.1103/PhysRevB.81.174528.

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We study the superfluid-insulator transition in a one-dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong-randomness real-space renormalization-group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid-insulator transition is always Kosterlitz-Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a nonuniversal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. 3, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott-glass phase. If both integer and half-integer filling factors are allowed then the corresponding phase is a random-singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.

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Additional Information:© 2010 The American Physical Society. Received 19 November 2009; revised manuscript received 20 April 2010; published 25 May 2010. We are most grateful to S. Girvin for the useful suggestion to look into the half-integer case first, and to D. S. Fisher, M. P. A. Fisher, T. Giamarchi, V. Gurarie, D. Huse, P. Le Doussal, O. Motrunich, N. Prokofe’v, and B. Svistunov for numerous discussions. A.P. acknowledges support from AFOSR YIP, NSF under Grant No. DMR-0907039, and the Sloan Foundation. G.R. acknowledges support of the Packard Foundation, Sloan Foundation and the Research Corporation. E.A. and Y.K. are grateful for support from the ISF. This work also benefited greatly from the BU visitor program (Y.K. and G.R.).
Funding AgencyGrant Number
Air Force Office of Scientific Research, Young Investigator Research Program (AFOSR YIP)UNSPECIFIED
Sloan FoundationUNSPECIFIED
Packard FoundationUNSPECIFIED
Research CorporationUNSPECIFIED
Issue or Number:17
Classification Code:PACS: 74.81.-g, 05.30.Jp.
Record Number:CaltechAUTHORS:20100616-075847387
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18697
Deposited By: Tony Diaz
Deposited On:09 Jul 2010 20:18
Last Modified:08 Nov 2021 23:46

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