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Physical Review Letters

Localization in interacting, disordered, Bose systems

Richard T. Scalettar, G. G. Batrouni, Gergely T. Zimányi

Published Jun 17, 1991• 281 citations
Publisher

Abstract

We use quantum Monte Carlo techniques to study a one-dimensional, disordered, interacting, Bose Hamiltonian. The effect of disorder on the Mott-insulator portion of the phase diagram is determined. We observe the destruction of superfluidity by disorder at incommensurate densities, for the first time demonstrating the emergence of a ``Bose-glass'' phase. In addition to these strong-coupling phases, we observe an unanticipated re-entrance into an Anderson-type localized regime for weak couplings.

DOI
10.1103/physrevlett.66.3144

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We use quantum Monte Carlo techniques to study a one-dimensional, disordered, interacting, Bose Hamiltonian. The effect of disorder on the Mott-insulator portion of the phase diagram is determined. We observe the destruction of superfluidity by disorder at incommensurate densities, for the first time demonstrating the emergence of a ``Bose-glass'' phase. In addition to these strong-coupling phases, we observe an unanticipated re-entrance into an Anderson-type localized regime for weak couplings.
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 investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered Boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a 1χ2 tail and the imaginary time Green's function decays algebraically C(τ) ≈ τ−1 giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate Boson densities we find direct Mott insulator to superfluid transition without an intervening Bose glass phase for weak disorder. For this transition we obtain the critical exponents z = 1, v = 0.7 ± 0.1 and η = 0.1 ± 0.1, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the tip of the Mott-lobes and that here the inequality v⩾2d is violated.
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 analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.
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We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.