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 $^4$He systems is an inhomogeneous dilute Bose gas, with almost all of the atoms occupying the same single-particle state at $T = 0$. Numerical evidence for this complete Bose-Einstein condensation was first given by the many-body variational calculations of $^4$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 $a$. At high densities, $n>>a^{-3}$, the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to $n^{2/3}$, 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 $n(p)$ of liquid $^4$He at $T=3D0^o$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 $^3$He, using fixed--node DMC, with nodes and trial functions provided by the EMC. In particular, we analyze the momentum distribution $n(p)$ with respect to the discontinuity $Z$ as well as the singular behavior, at the Fermi surface. We also show that an approximate factorization of the one-body density matrix $\rho(r)\simeq \rho_0(r)\rho_B(r)$ holds, with $\rho_0(r)$ and $\rho_B(r)$ respectively the density matrix of the ideal Fermi gas and the density matrix of a Bose $^3$He.Comment: 10 pages, REVTeX, 12 figure