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Cited by 3,512Cold Atom Physics and Bose-Einstein CondensatesTheoretical and Computational PhysicsQuantum many-body systems

Boson localization and the superfluid-insulator transition

Fisher, Matthew P. A., Weichman, Peter B., Grinstein, G., Fisher, Daniel S.·1989·Physical Review B
DOI 10.1103/physrevb.40.546
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Abstract

The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator 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 particle-hole 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 particle-hole 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 zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} 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 order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension ${d}_{c}$ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on $^{4}\mathrm{He}$ absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.

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  • All models within a given universality class give rise to the same collective behavior at large distances, irrespective of microscopic details, and are characterized by the same critical exponents.

    “All models within a given universality class give rise to the same collective behavior at large distances (typically large with respect to the lattice spacing), irrespective of their microscopic details [177]. Therefore, all relevant thermodynamic quantities for all models within a class are characterized by the same small set of critical exponents which describe the power-law decay of the”

    From Can one trust quantum simulators? (2012) · cites this paper as [177]

  • Disorder can have a significant effect on relevant quantities that one could hope to extract from the simulator, such as critical points and exponents, or its central charge if described by a conformal field theory.

    “In particular, disorder can have a significant effect on relevant quantities that one could hope to extract from the simulator, such as critical points and exponents, or - if the system is described by a conformal field theory (CFT) - its central charge [177].”

    From Can one trust quantum simulators? (2012) · cites this paper as [177]

  • Without disorder, the correlation length scaling follows a universal function f, allowing extraction of the critical exponent ν from a data collapse of the correlations.

    “Without disorder, <!-- formula-not-decoded --> for some universal function f [177]. Hence, one can extract the critical exponent for the correlation length ν from a data collapse of the correlations.”

    From Can one trust quantum simulators? (2012) · cites this paper as [177]

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Authors
Fisher, M. P. A., Weichman, P. B., Grinstein, G., & Fisher, D. S.
Affiliations
  • IBM Research - Thomas J. Watson Research Center (US)
  • California Institute of Technology (US)
  • Princeton University (US)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1989-07-01
Volume
40
Issue
1
Pages
546-570
ISSN
0163-1829 (ISSN-L)
DOI
10.1103/physrevb.40.546
OpenAlex
W1967336145
Cited by
3,512
References
34
Citations by year
2026: 56 · 2025: 87 · 2024: 94 · 2023: 100 · 2022: 107 · 2021: 109 · 2020: 111 · 2019: 107 · 2018: 124 · 2017: 144 · 2016: 143 · 2015: 154 · 2014: 144 · 2013: 172 · 2012: 159
FWCI
14.55
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B, Condensed matter (publishedVersion)
  • PubMed (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
superfluid-insulator transition, Bose glass, Mott insulator, periodic potential, random potential, disorder, superfluid density, dynamical exponent, critical exponents, upper critical dimension, renormalization group, quantum fluctuations, XY model, one-dimensional bosons, zero-temperature phase transition, Bose-Hubbard model

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