Fisher, Matthew P. A. and Weichman, Peter B. and Grinstein, G. and Fisher, Daniel S. (1989) Boson localization and the superfluidinsulator transition. Physical Review B, 40 (1). pp. 546570. ISSN 01631829. http://resolver.caltech.edu/CaltechAUTHORS:FISprb89

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Abstract
The phase diagrams and phase transitions of bosons with shortranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluidinsulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particlehole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ‘‘ideal,’’ or mean field in character, but at special multicritical points with particlehole symmetry it is in the universality class of the (d+1)dimensional XY model. In the presence of disorder, a third, ‘‘Bose glass’’ phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential. The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zerotemperature superfluidinsulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary λ transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and orderparameter correlation exponents ν and η which satisfy the bounds ν≥2/d and η≤2d, respectively. It is argued that the superfluidinsulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalizationgroup calculation wherein the critical exponents have meanfield values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of onedimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the λ transition temperature to the zerotemperature superfluid density is found to be d/2(d1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
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Additional Information:  ©1989 The American Physical Society Received 15 November 1988 We are very grateful to K. Blum, M.C. Cross, S.M. Girvin, B.I. Halperin, D.H. Lee, P.A. Lee, J. Reppy, D. Rokhsae, N. Schick, and J. Toner for useful discussions. Thanks are also due to the Aspen Center for Physics where this work was begun. P.B.W. gratefully acknowledges financial support from the Weingart Foundation through Caltech and the National Science Foundation (NSF) through Grant No. DMR8412543. D.S.F. gratefully acknowledges the support of the A.P.Solan Foundation and the NSF under Grant No. DMR8719523. 
Record Number:  CaltechAUTHORS:FISprb89 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:FISprb89 
Alternative URL:  http://dx.doi.org/10.1103/PhysRevB.40.546 
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Deposited On:  14 Dec 2006 
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