Superfluid clusters, percolation and phase transitions in the disordered, two-dimensional Bose–Hubbard model

2013/04/18 by A E Niederle, Astrid Niederle, Heiko Rieger +1 · 47 citations
Physics and Astronomy · #Boson #Cluster (spacecraft) #Cold Atom Physics and Bose-Einstein Condensates #Context (archaeology) #Mean field theory #Percolation (cognitive psychology) #Phase (matter) #Phase diagram #Phase transition #Physics of Superconductivity and Magnetism #Quantum many-body systems #Superfluidity #cond-mat.dis-nn #cond-mat.quant-gas #cond-mat.stat-mech

paper · pdf · doi:10.1088/1367-2630/15/7/075029

published in New Journal of Physics 15(7), 075029 (IOP Publishing) · 27 pages, 9 figures

arxiv created 2013/04/18 · openalex publication_date 2013/07/30 · arxiv updated 2013/08/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Bose glass (BG) phase is the Griffiths region of the disordered Bose–Hubbard model (BHM), characterized by finite, quasi-superfluid clusters within a Mott insulating background. We propose to utilize this characterization to identify the complete zero-temperature phase diagram of the disordered BHM in d ⩾ 2 dimensions by analysing the geometric properties of what we call superfluid (SF) clusters, which are defined to be clusters of sites with non-integer expectation values for the local boson occupation number. The Mott insulator phase then is the region in the phase diagram where no SF clusters exist, and the SF phase the region where SF clusters percolate—the BG phase is inbetween: SF clusters exist, but do not percolate. This definition is particularly useful in the context of local mean field (LMF) or Gutzwiller–Ansatz calculations, where we show that an identification of the phases on the basis of global quantities such as the averaged SF order parameter and the compressibility is misleading. We apply the SF cluster analysis to the LMF ground states of the two-dimensional disordered BHM to produce its phase diagram and find (a) an excellent agreement with the phase diagram predicted on the basis of quantum Monte Carlo simulations for the commensurate density n = 1 and (b) large differences to stochastic mean field and other mean field predictions for fixed disorder strength. The relation of the percolation transition of the SF clusters with the onset of non-vanishing SF stiffness indicating the BG to SF transition is discussed.

Citations

• Mean-field phase diagram of cold lattice bosons in disordered potentials
• Weakly interacting Bose gas in a random environment
• Superfluid-Insulator Transition in Commensurate Disordered Bosonic Systems: Large-Scale Worm Algorithm Simulations
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• Phase diagram for ultracold bosons in optical lattices and superlattices
• Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level