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Physical review. B, Condensed matter

Monte Carlo simulation of hard-core bosons on a three-dimensional lattice

Morten Holm Pedersen, T. Schneider

Published Mar 1, 1996• 5 citations
Publisher

Abstract

A model of hard-core bosons on a three-dimensional (3D) lattice has been studied using both quantum Monte Carlo and classical Monte Carlo techniques. We have calculated the transition temperature for Bose-Einstein condensation, the zero-temperature penetration depth and the specific-heat critical amplitude, and have explored the hyperuniversal scaling relationship between these quantities pertaining to the expected 3D XY critical point. As a conclusion we draw a phenomenological analogy between the model studied and extreme type-II superconductors. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.5826

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A model of hard-core bosons on a three-dimensional (3D) lattice has been studied using both quantum Monte Carlo and classical Monte Carlo techniques. We have calculated the transition temperature for Bose-Einstein condensation, the zero-temperature penetration depth and the specific-heat critical amplitude, and have explored the hyperuniversal scaling relationship between these quantities pertaining to the expected 3D XY critical point. As a conclusion we draw a phenomenological analogy between the model studied and extreme type-II superconductors. \textcopyright{} 1996 The American Physical Society.
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
A path-integral quantum Monte Carlo method is used to calculate finite temperature properties of up to 1000 hard-core bosons in a two-dimensional isotropic harmonic-oscillator potential. If the interatomic repulsions are sufficiently short range, an abrupt increase in the condensate fraction and a hump in the specific heat occur close to the critical temperature of ideal bosons. The critical temperature and the condensate fraction are in general lowered by an increase in the hard-core radius a. If a is decreased below a certain level, the condensate fraction becomes indistinguishable from the corresponding value of the ideal bosons. For up to 1000 particles, this occurs when ${\mathrm{ln}}^{\ensuremath{-}1}{(1/na}^{2})\ensuremath{\lesssim}0.1,$ where n is the average particle density.
Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons (XYXYXY model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.
In this study, we reveal nontrivial quantum physics in an infinite-temperature system. By performing an unbiased quantum Monte Carlo simulation, we study a hybrid model composed of hard-core bosons, whose hopping amplitude is mediated by the density of another type of soft-core bond bosons that can absorb entropy indefinitely. It is shown that the Bose-Einstein condensate can persist in three dimensions even when the temperature approaches the infinite-temperature limit. In contrast, in two dimensions, the quasi-superfluid is depleted by the fluctuations of the bond bosons, which, on the other hand, enhance the conductivity of the hard-core bosons in the normal phase. A generalization to the fermionic model has also been discussed.
We study the three-dimensional bosonic ttt-JJJ model, that is, the ttt-JJJ model of ``bosonic electrons'' at finite temperatures. This model describes a system of an isotropic antiferromagnet with doped bosonic holes and is closely related to systems of two-component bosons in an optical lattice. The bosonic ``electron'' operator ${B}_{x\ensuremath{\sigma}}$ at the site xxx with a two-component spin $\ensuremath{\sigma}(=$1,2)1,2)1,2) is treated as a hard-core boson operator and represented by a composite of two slave particles: a spinon described by a Schwinger boson (CP1{}^{1}1 boson) ${z}_{x\ensuremath{\sigma}}$ and a holon described by a hard-core-boson field ${\ensuremath{\phi}}_{x}$ as ${B}_{x\ensuremath{\sigma}}={\ensuremath{\phi}}_{x}^{\ifmmode\dagger\else\textdagger\fi{}}{z}_{x\ensuremath{\sigma}}$. By means of Monte Carlo simulations of this bosonic ttt-JJJ model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. Obtained results show that the bosonic ttt-JJJ model has a phase diagram that suggests some interesting implications for high-temperature superconducting materials.