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arXiv:0903.2537

Quantum Monte Carlo simulations for the Bose-Hubbard model with random chemical potential; localized Bose-Einstein condensation without superfluidity

M. Tsukamoto, Makoto Tsubota

Published Mar 14, 2009• 0 citations
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Abstract

The hardcore-Bose-Hubbard model with random chemical potential is investigated using quantum Monte Carlo simulation. We consider two cases of random distribution of the chemical potential: a uniformly random distribution and a correlated distribution. The temperature dependences of the superfluid density, the specific heat, and the correlation functions are calculated. If the distribution of the randomness is correlated, there exists an intermediate state, which can be thought of as a localized condensate state of bosons, between the superfluid state and the normal state.

DOI
10.48550/arxiv.0903.2537

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We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T 2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T =0 Gross–Pitaevskii theory, even in the regime of very strong disorder.
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.
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