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Physical review. B, Condensed matter

World-line quantum Monte Carlo algorithm for a one-dimensional Bose model

G. G. Batrouni, Richard T. Scalettar

Published Oct 1, 1992• 173 citations
Publisher

Abstract

In this paper we provide a detailed description of the ground-state phase diagram of interacting, disordered bosons on a lattice. We describe a quantum Monte Carlo algorithm that incorporates in an efficient manner the required bosonic wave-function symmetry. We consider the ordered case, where we evaluate the compressibility gap and show the lowest three Mott insulating lobes. We obtain the critical ratio of interaction strength to hopping at which the onset of superfluidity occurs for the first lobe, and the critical exponents \ensuremath{\nu} and z. For the disordered model we show the effect of randomness on the phase diagram and the superfluid correlations. We also measure the response of the superfluid density, ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, to external perturbations. This provides an unambiguous characterization of the recently observed Bose and Anderson glass phases.

DOI
10.1103/physrevb.46.9051

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In this paper we provide a detailed description of the ground-state phase diagram of interacting, disordered bosons on a lattice. We describe a quantum Monte Carlo algorithm that incorporates in an efficient manner the required bosonic wave-function symmetry. We consider the ordered case, where we evaluate the compressibility gap and show the lowest three Mott insulating lobes. We obtain the critical ratio of interaction strength to hopping at which the onset of superfluidity occurs for the first lobe, and the critical exponents \ensuremath{\nu} and z. For the disordered model we show the effect of randomness on the phase diagram and the superfluid correlations. We also measure the response of the superfluid density, \ensuremathρs{\mathrm{\ensuremath{\rho}}}_{\mathit{s}}\ensuremathρs​, to external perturbations. This provides an unambiguous characterization of the recently observed Bose and Anderson glass phases.
We study the two-dimensional disordered boson Hubbard model via quantum Monte Carlo simulations. It is shown that the probability distribution of the local susceptibility has a 1/${\mathrm{\ensuremath{\chi}}}^{2}$ tail in the Bose-glass phase. This gives rise to a divergence although particles are completely localized here as we prove with the help of the participation ratio. We demonstrate the presence of an incompressible Mott lobe within the Bose-glass phase and show that a direct Mott-insulator-to-superfluid transition happens at the tip of the lobe. Here we find critical exponents z=1, \ensuremath{\nu}\ensuremath{\sim}0.7 and \ensuremath{\eta}\ensuremath{\sim}0.1, which agree with those of the pure three-dimensional classical XY model.
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.
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.
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 study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.