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arXiv:1804.05789 · Physical Review A

Properties of the superfluid in the disordered Bose-Hubbard model

Bruno Ricardi de Abreu, Ushnish Ray, S. A. Vitiello, David M. Ceperley

Published Aug 27, 2018• 11 citations
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Abstract

We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using quantum Monte Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the reentrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. Despite this, both the superfluid fraction and compressibility remain self-averaging throughout the superfluid phase. Close to the superfluid--Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. Our results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not possible.

DOI
10.1103/physreva.98.023628

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We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
We study by numerical simulation a disordered Bose-Hubbard model in low-dimensional lattices. We show that a proper characterization of the phase diagram on finite disordered clusters requires the knowledge of probability distributions of physical quantities rather than their averages. This holds in particular for determining the stability region of the Bose-glass phase, the compressible but not superfluid phase that exists whenever disorder is present. This result suggests that a similar statistical analysis should be performed also to interpret experiments on cold gases trapped in disordered lattices, limited as they are to finite sizes.
We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder, and the quantum critical point between the Bose glass and superfluid is determined in the grand canonical ensemble at $\ensuremath{\mu}/U=0$ (close to $\ensuremath{\rho}=0.5$), $\ensuremath{\mu}/U=0.375$ (close to $\ensuremath{\rho}=1$), and $\ensuremath{\mu}/U=1$ as well as in the canonical ensemble at $\ensuremath{\rho}=0.5$ and 1. Particular attention is paid to disorder averaging, and it is shown that a large number of disorder realizations are needed in order to obtain reliable results. Typically, more than 100000100\phantom{\rule{0.16em}{0ex}}000100000 disorder realizations were used. In the grand canonical ensemble, we find Ztc/U=0.112(1)Z{t}_{c}/U=0.112(1)Ztc​/U=0.112(1) with $\ensuremath{\mu}/U=0.375$, significantly different from previous studies. When compared to the critical point in the absence of disorder (Ztc/U=0.2385Z{t}_{c}/U=0.2385Ztc​/U=0.2385), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, we then study the dynamic conductivity.
We study the equilibrium properties of the one-dimensional disordered Bose–Hubbard model by means of a gauge-adaptive tree tensor network variational method suitable for systems with periodic boundary conditions. We compute the superfluid stiffness and superfluid correlations close to the superfluid to glass transition line, obtaining accurate locations of the critical points. By studying the statistics of the exponent of the power-law decay of the correlation, we determine the boundary between the superfluid region and the Bose glass phase in the regime of strong disorder and in the weakly interacting region, not explored numerically before. In the former case our simulations are in agreement with previous Monte Carlo calculations.
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.