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Progress of Theoretical Physics Supplement

Boson Localization on the Superfluid-Insulator Transition by Quantum Monte Calro Simulation

Masahito Hashimoto, Masako Takasu

Published Jan 1, 2000• 1 citation
Publisher

Abstract

For some systems in critical phenomena, Monte Carlo (MC) simulations using conventional algorithm are inefficient, because of long correlation between successive MC configurations. Our system in Eq. (1) suffers this difficulty in critical region between superfluid phase and glass insulator phase. The loop algorithm overcomes this difficulty. We try to apply this algorithm to the soft core boson system, and carry out calculations with random boson Hubbard model.

DOI
10.1143/ptps.138.529

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For some systems in critical phenomena, Monte Carlo (MC) simulations using conventional algorithm are inefficient, because of long correlation between successive MC configurations. Our system in Eq. (1) suffers this difficulty in critical region between superfluid phase and glass insulator phase. The loop algorithm overcomes this difficulty. We try to apply this algorithm to the soft core boson system, and carry out calculations with random boson Hubbard model.
We study the superfluid-insulator transition of the 2-D boson system on random surfaces. Using quantum Monte Carlo simulation and grand-canonical ensemble, we investigate the random Hubbard model and study the phase transition between the superfluid phase and the Bose glass insulator phase. Changing the chemical potential µ, we observe the transition from the superfluid phase to the insulator phase. We show the dimensional dependence of the transition by comparing the results of 2-D and 1-D boson systems. To study the localization of the boson paths, we perform the simulation on the anisotropic surfaces, and discuss the crossover from 2-D system to 1-D system.
We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N a =50 sites is already sufficient to estimate the thermodynamic value of the critical quantity ( t/U ) c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, ( t/U ) c =0.300±0.005, agrees with the value ( t/U ) c =0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[− b (1− t/t c ) −1/2 ].
A review of the loop algorithm , its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a quantum Monte Carlo procedure that employs non-local changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion. It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal fields. The method has been applied successfully to a variety of models for spin and charge degrees of freedom, including Heisenberg and XYZ spin models, hard-core bosons, Hubbard and t - J -models. Owing to the improved efficiency, precise calculations of asymptotic behaviour and of quantum critical exponents have been possible.
We introduce two quantum Monte Carlo algorithms and employ them to study the superfluid-insulator transition in a two-dimensional system of hard-core bosons. One of the algorithms is appropriate for zero temperature and is based upon the Green's function Monte Carlo method; the other is an extension of the finite-temperature world-line cluster method. In each case we find that the dynamical exponent is consistent with the theoretical prediction of z=2z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2z=2 by Fisher and co-workers.