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

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.