77 research outputs found
Ab Initio Calculations of the Spin-Half XY Model
In this article, the correlated basis-function (CBF) method is applied for
the first time to the quantum spin-half {\it XY} model on the linear chain, the
square lattice, and the simple cubic lattice. In this treatment of the quantum
spin-half {\it XY} model a Jastrow ansatz is utilised to approximate the
ground-state wave function. Results for the ground-state energy and the
sublattice magnetisation are presented, and evidence that the CBF detects the
quantum phase transition point in this model is also presented. The CBF results
are compared to previous coupled cluster method (CCM) results for the spin-half
{\it XY} model, and the two formalisms are then compared and contrasted.Comment: 10 pages, 3 figure
Ab Initio Treatments of the Ising Model in a Transverse Field
In this article, new results are presented for the zero-temperature
ground-state properties of the spin-half transverse Ising model on various
lattices using three different approximate techniques. These are, respectively,
the coupled cluster method, the correlated basis function method, and the
variational quantum Monte Carlo method. The methods, at different levels of
approximation, are used to study the ground-state properties of these systems,
and the results are found to be in excellent agreement both with each other and
with results of exact calculations for the linear chain and results of exact
cumulant series expansions for lattices of higher spatial dimension. The
different techniques used are compared and contrasted in the light of these
results, and the constructions of the approximate ground-state wave functions
are especially discussed.Comment: 28 Pages, 4 Figures, 1 Tabl
Number--conserving model for boson pairing
An independent pair ansatz is developed for the many body wavefunction of
dilute Bose systems. The pair correlation is optimized by minimizing the
expectation value of the full hamiltonian (rather than the truncated Bogoliubov
one) providing a rigorous energy upper bound. In contrast with the Jastrow
model, hypernetted chain theory provides closed-form exactly solvable equations
for the optimized pair correlation. The model involves both condensate and
coherent pairing with number conservation and kinetic energy sum rules
satisfied exactly and the compressibility sum rule obeyed at low density. We
compute, for bulk boson matter at a given density and zero temperature, (i) the
two--body distribution function, (ii) the energy per particle, (iii) the sound
velocity, (iv) the chemical potential, (v) the momentum distribution and its
condensate fraction and (vi) the pairing function, which quantifies the ODLRO
resulting from the structural properties of the two--particle density matrix.
The connections with the low--density expansion and Bogoliubov theory are
analyzed at different density values, including the density and scattering
length regime of interest of trapped-atoms Bose--Einstein condensates.
Comparison with the available Diffusion Monte Carlo results is also made.Comment: 21 pages, 12 figure
Static structure factor of liquid parahydrogen
7 págs.; 5 figs. ; PACS number~s!: 61.20.2p, 61.12.2q, 78.70.2gThe single-differential neutron-scattering cross section of liquid parahydrogen has been measured at 15.2 K and 2 bars of applied pressure by means of low-energy neutron diffraction. Our experimental conditions enable the direct observation of the peak of the liquid structure factor and therefore largely improve the signal-to-noise ratio with respect to measurements carried out using higher-energy neutron diffraction. This avoids the need of performing corrections of approximate nature to the measured cross section that is dominated by molecular rotational components if measured by conventional neutron diffraction. ©2004 American Physical SocietyPeer Reviewe
Surface Region of Superfluid Helium as an Inhomogeneous Bose-Condensed Gas
We present arguments that the low density surface region of self-bounded
superfluid He systems is an inhomogeneous dilute Bose gas, with almost all
of the atoms occupying the same single-particle state at . Numerical
evidence for this complete Bose-Einstein condensation was first given by the
many-body variational calculations of He droplets by Lewart, Pandharipande
and Pieper in 1988. We show that the low density surface region can be treated
rigorously using a generalized Gross-Pitaevskii equation for the Bose order
parameter.Comment: 4 pages, 1 Postscript figur
Cold Bose gases with large scattering lengths
We calculate the energy and condensate fraction for a dense system of bosons
interacting through an attractive short range interaction with positive s-wave
scattering length . At high densities, , the energy per particle,
chemical potential, and square of the sound speed are independent of the
scattering length and proportional to , as in Fermi systems.Comment: 4 pages, 3 figure
Quantum phase transitions and thermodynamic properties in highly anisotropic magnets
The systems exhibiting quantum phase transitions (QPT) are investigated
within the Ising model in the transverse field and Heisenberg model with
easy-plane single-site anisotropy. Near QPT a correspondence between parameters
of these models and of quantum phi^4 model is established. A scaling analysis
is performed for the ground-state properties. The influence of the external
longitudinal magnetic field on the ground-state properties is investigated, and
the corresponding magnetic susceptibility is calculated. Finite-temperature
properties are considered with the use of the scaling analysis for the
effective classical model proposed by Sachdev. Analytical results for the
ordering temperature and temperature dependences of the magnetization and
energy gap are obtained in the case of a small ground-state moment. The forms
of dependences of observable quantities on the bare splitting (or magnetic
field) and renormalized splitting turn out to be different. A comparison with
numerical calculations and experimental data on systems demonstrating magnetic
and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure
Momentum distribution of liquid helium
We have obtained the one--body density matrix and the momentum distribution
of liquid He at K from Diffusion Monte Carlo (DMC)
simulations, using trial functions optimized via the Euler Monte Carlo (EMC)
method. We find a condensate fraction smaller than in previous calculations.
Though we do not explicitly include long--range correlations in our
calculations, we get a momentum distribution at long wavelength which is
compatible with the presence of long--range correlations in the exact wave
function. We have also studied He, using fixed--node DMC, with nodes and
trial functions provided by the EMC. In particular, we analyze the momentum
distribution with respect to the discontinuity as well as the
singular behavior, at the Fermi surface. We also show that an approximate
factorization of the one-body density matrix
holds, with and respectively the density matrix of the
ideal Fermi gas and the density matrix of a Bose He.Comment: 10 pages, REVTeX, 12 figure
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