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arXiv:cond-mat/9409112 · Physical Review Letters

Quantum Simulations of the Superfluid-Insulator Transition for Two-Dimensional, Disordered, Hard-Core Bosons

Shiwei Zhang, Naoki Kawashima, Joseph Carlson, James E. Gubernatis

Published Feb 27, 1995• 67 citations
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Abstract

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 $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ by Fisher and co-workers.

DOI
10.1103/physrevlett.74.1500

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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.
The ground-state of hard-core bosons in a random one-body potential is studied numerically to observe the transition from superfluid to insulating ``Bose glass'' phase. Finite-size scaling analyses are performed to estimate the transition point and critical exponents. The dynamical critical exponent is z=1.95\ifmmode\pm\else\textpm\fi{}0.25 and is consistent with the prediction of Fisher et al. [Phys. Rev. B 40, 546 (1989)]. Values for other exponents and preliminary results regarding the universal conductivity are presented.
Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite-temperature Kosterlitz-Thouless transition. The relationship between low-temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
We study the superfluid density of hard-core bosons on quasi-one-dimensional lattices using the quantum Monte Carlo method. Because of phase slippage, the superfluid density drops quickly to zero at finite temperatures with increasing the system length $\ensuremath{\ell}$ and the superfluid transition temperature is zero in one spatial dimension and also in quasi-one dimension in the limit of $\ensuremath{\ell}\ensuremath{\rightarrow}\ensuremath{\infty}$. We calculate the superfluid density of a model where no phase slippage is allowed and show that the superfluid density remains finite at finite temperatures even in the one-dimensional limit. We also discuss how finite superfluid density can be observed in a quasi-one-dimensional system using a torsional oscillator.
We study the T=0 critical properties of the superfluid-insulator transition in 2D hard core Bose systems with disorder. Using quantum Monte Carlo simulations and finite size scaling on 64\ifmmode\times\else\texttimes\fi{}64 lattices we find the dynamical exponent z=0.5\ifmmode\pm\else\textpm\fi{}0.1 and the correlation length exponent \ensuremath{\nu}=2.2\ifmmode\pm\else\textpm\fi{}0.2. At the transition, the system is metallic with a conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathit{c}}$=(1.2\ifmmode\pm\else\textpm\fi{}0.2)(e∗{\mathit{e}}^{\mathrm{*}}e∗)2{)}^{2})2/h and a nonzero compressibility \ensuremath{\kappa}\ensuremath{\ne}0. These conclusions differ from the existing scaling theory as well as from simulations on simplified models argued to be in the same universality class. Our results are suggestive of new low lying collective excitations (modified from usual phonons) in the disordered system.
We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.35\ifmmode\pm\else\textpm\fi{}0.05$ and the correlation length critical exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.67\ifmmode\pm\else\textpm\fi{}0.03$. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.
The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters ( t x = t p , t y < 0), the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case t x , t y , t p > 0, the system is exactly studied using quantum Monte Carlo (QMC) method without a sign problem. It is found that the system is a Mott insulator for small t p and a quantum phase transition to a superfluid phase is driven by increasing t p . The critical t p c is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments.