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arXiv:cond-mat/0603571

Identifying the Bose glass phase

Rami Pugatch, Nir Bar‐Gill, Nadav Y. Katz, Eitan E. Rowen, Nir Davidson

Published Mar 22, 2006• 3 citations
arXivHTMLPDF

Abstract

Introducing disorder into the Bose-Hubbard model at integer fillings leads to a Bose glass phase, along with the Mott insulator and superfluid phases. We suggest a new order parameter: the determinant of the one body density matrix, which is nonzero only within the Mott-insulator phase. Alongside the superfluid fraction, it is then possible to distinguish the three phases. The Bose glass phase is the only phase which has vanishing determinant and superfluid fraction. The vanishing of the determinant in the Bose glass phase occurs due to the partial fragmentation of the condensate into localized fragments, each with zero superfluid response, which implies the presence of unoccupied sites and hence the presence of lines of zeros in the one body density matrix. In the superfluid phase, the determinant vanish for another reason - due to the macroscopic occupation of a single particle state. Finally, we suggest the enhancement of the three body decay rate in the Bose glass phase, as an experimental indicator for the presence of localized fragments.

DOI
10.48550/arxiv.cond-mat/0603571

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Introducing disorder into the Bose-Hubbard model at integer fillings leads to a Bose glass phase, along with the Mott insulator and superfluid phases. We suggest a new order parameter: the determinant of the one body density matrix, which is nonzero only within the Mott-insulator phase. Alongside the superfluid fraction, it is then possible to distinguish the three phases. The Bose glass phase is the only phase which has vanishing determinant and superfluid fraction. The vanishing of the determinant in the Bose glass phase occurs due to the partial fragmentation of the condensate into localized fragments, each with zero superfluid response, which implies the presence of unoccupied sites and hence the presence of lines of zeros in the one body density matrix. In the superfluid phase, the determinant vanish for another reason - due to the macroscopic occupation of a single particle state. Finally, we suggest the enhancement of the three body decay rate in the Bose glass phase, as an experimental indicator for the presence of localized fragments.
We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.
We study the effects of disorder on the spin dependent interaction term of a spinor Bose Hubbard model with a three body interaction potential. The signature of the Bose glass (BG) phase is observed by computing the fraction of the lattice sites having finite superfluid (SF) order parameter and non integer occupation densities. We obtain the phase diagram both for the antiferromagnetic (AF) and ferromagnetic (F) cases via a percolation analysis. In the AF case, the BG phase intervenes between the odd-even Mott insulating (MI) lobes (for example, the lobes corresponding to occupation densities, n=1 and (n=2) but not between the even-odd MI lobes. In the ferromagnetic case, the presence of the BG phase is observed between all the MI lobes irrespective of them being even or odd. The BG phase almost destroys the first MI lobe while the MI phase looks more stable than the SF phase both in the AF and F cases due to the presence of the three body interactions.
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.
We perform a matrix-product-state–based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities , 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come for free when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when and 1/2 (without the Mott insulator) as found in previous studies. For the system we find a double-lobed superfluid phase with possible re-entrance.
We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet et al. [Phys. Rev. Lett. 103, 140402 (2009)] states that the Bose-glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a regular gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly nontrivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.
The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.