589 research outputs found
Exact ground state Monte Carlo method for Bosons without importance sampling
Generally ``exact'' Quantum Monte Carlo computations for the ground state of
many Bosons make use of importance sampling. The importance sampling is based,
either on a guiding function or on an initial variational wave function. Here
we investigate the need of importance sampling in the case of Path Integral
Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time
evolution of an initial wave function with a non zero overlap with the ground
state, that gives rise to a discrete path which is sampled via a Metropolis
like algorithm. In principle the exact ground state is reached in the limit of
an infinite imaginary time evolution, but actual computations are based on
finite time evolutions and the question is whether such computations give
unbiased exact results. We have studied bulk liquid and solid 4He with PIGS by
considering as initial wave function a constant, i.e. the ground state of an
ideal Bose gas. This implies that the evolution toward the ground state is
driven only by the imaginary time propagator, i.e. there is no importance
sampling. For both the phases we obtain results converging to those obtained by
considering the best available variational wave function (the Shadow wave
function) as initial wave function. Moreover we obtain the same results even by
considering wave functions with the wrong correlations, for instance a wave
function of a strongly localized Einstein crystal for the liquid phase. This
convergence is true not only for diagonal properties such as the energy, the
radial distribution function and the static structure factor, but also for
off-diagonal ones, such as the one--body density matrix. From this analysis we
conclude that zero temperature PIGS calculations can be as unbiased as those of
finite temperature Path Integral Monte Carlo.Comment: 11 pages, 10 figure
Ground State Properties of Fermi Gases in the Strongly Interacting Regime
The ground state energies and pairing gaps in dilute superfluid Fermi gases
have now been calculated with the quantum Monte Carlo method without detailed
knowledge of their wave functions. However, such knowledge is essential to
predict other properties of these gases such as density matrices and pair
distribution functions. We present a new and simple method to optimize the wave
functions of quantum fluids using Green's function Monte Carlo method. It is
used to calculate the pair distribution functions and potential energies of
Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer
superfluid to molecular Bose-Einstein condensation, spanned as the interaction
strength is varied.Comment: 4 pages, 4 figure
Diagrammatic approach in the variational coupled-cluster method
Recently, as demonstrated by an antiferromagnetic spin-lattice application,
we have successfully extended the coupled-cluster method (CCM) to a variational
formalism in which two sets of distribution functions are introduced to
evaluate Hamiltonian expectation. We calculated these distribution functions by
employing an algebraic scheme. Here we present an alternative calculation based
on a diagrammatic technique. Similar to the method of correlated-basis
functionals (CBF), a generating functional is introduced and calculated by a
linked-cluster expansion in terms of diagrams which are categorized and
constructed according to a few simple rules and using correlation coefficients
and Pauli exclusion principle (or Pauli line) as basic elements. Infinite
resummations of diagrams can then be done in a straightforward manner. One such
resummation, which includes all so-called ring diagrams and ignores Pauli
exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond
SWT are also given. Interestingly, one such approximation including all
so-called super-ring diagrams by a resummation of infinite Pauli lines in
additional to resummations of ring diagrams produces a convergent, precise
number for the order-parameter of the one-dimensional isotropic model, contrast
to the well-known divergence of SWT. We also discuss the direct relation
between our variational CCM and CBF and discuss a possible unification of the
two theories.Comment: 18 pages, 9 figure
Separable form of low-momentum realistic NN interaction
The low-momentum interaction derived from realistic models
of the nucleon-nucleon interaction is presented in a separable form. This
separable force is supported by a contact interaction in order to achieve the
saturation properties of symmetric nuclear matter. Bulk properties of nuclear
matter and finite nuclei are investigated for the separable form of
and two different parameterizations of the contact term. The
accuracy of the separable force in Hartree-Fock calculations with respect to
the original interaction is discussed. For a cutoff
parameter of 2 fm a representation by a rank 2 separable force
yields a sufficient accuracy, while higher ranks are required for larger
cut-off parameters. The resulting separable force is parameterized in a simple
way to allow for an easy application in other nuclear structure calculations.Comment: 11 pages, 7 figure
Many-Body Theory of the Electroweak Nuclear Response
After a brief review of the theoretical description of nuclei based on
nonrelativistic many-body theory and realistic hamiltonians, these lectures
focus on its application to the analysis of the electroweak response. Special
emphasis is given to electron-nucleus scattering, whose experimental study has
provided a wealth of information on nuclear structure and dynamics, exposing
the limitations of the shell model. The extension of the formalism to the case
of neutrino-nucleus interactions, whose quantitative understanding is required
to reduce the systematic uncertainty of neutrino oscillation experiments, is
also discussed.Comment: Lectures delivered at the DAE-BRNS Workshop on Hadron Physics.
Aligarh Muslim University, Aligarh (India), February 18-23, 200
Ground state properties of a dilute homogeneous Bose gas of hard disks in two dimensions
The energy and structure of a dilute hard-disks Bose gas are studied in the
framework of a variational many-body approach based on a Jastrow correlated
ground state wave function. The asymptotic behaviors of the radial distribution
function and the one-body density matrix are analyzed after solving the Euler
equation obtained by a free minimization of the hypernetted chain energy
functional. Our results show important deviations from those of the available
low density expansions, already at gas parameter values . The
condensate fraction in 2D is also computed and found generally lower than the
3D one at the same .Comment: Submitted to PRA. 7 pages and 8 figure
Pair Excitations and Vertex Corrections in Fermi Fluids
Based on an equations--of--motion approach for time--dependent pair
correlations in strongly interacting Fermi liquids, we have developed a theory
for describing the excitation spectrum of these systems. Compared to the known
``correlated'' random--phase approximation (CRPA), our approach has the
following properties: i) The CRPA is reproduced when pair fluctuations are
neglected. ii) The first two energy--weighted sumrules are fulfilled implying a
correct static structure. iii) No ad--hoc assumptions for the effective mass
are needed to reproduce the experimental dispersion of the roton in 3He. iv)
The density response function displays a novel form, arising from vertex
corrections in the proper polarisation. Our theory is presented here with
special emphasis on this latter point. We have also extended the approach to
the single particle self-energy and included pair fluctuations in the same way.
The theory provides a diagrammatic superset of the familiar GW approximation.
It aims at a consistent calculation of single particle excitations with an
accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug.
2006, Kyoto, Japa
Excited states of quantum many-body interacting systems: A variational coupled-cluster description
We extend recently proposed variational coupled-cluster method to describe
excitation states of quantum many-body interacting systems. We discuss, in
general terms, both quasiparticle excitations and quasiparticle-density-wave
excitations (collective modes). In application to quantum antiferromagnets, we
reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of
spin . In addition, we obtain new, spin-zero magnon-density-wave
excitations which has been missing in Anserson's spin-wave theory. Implications
of these new collective modes are discussed.Comment: 17 pages, 4 figure
Soluble `Supersymmetric' Quantum XY Model
We present a `supersymmetric' modification of the -dimensional quantum
rotor model whose ground state is exactly soluble. The model undergoes a
vortex-binding transition from insulator to metal as the rotor coupling is
varied. The Hamiltonian contains three-site terms which are relevant: they
change the universality class of the transition from that of the ()--- to
the -dimensional classical XY model. The metallic phase has algebraic ODLRO
but the superfluid density is identically zero. Variational wave functions for
single-particle and collective excitations are presented.Comment: 12 pages, REVTEX 3.0, IUCM93-00
Dynamic Many-Body Theory. II. Dynamics of Strongly Correlated Fermi Fluids
We develop a systematic theory of multi-particle excitations in strongly
interacting Fermi systems. Our work is the generalization of the time-honored
work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most
advanced implementation, quantitative predictions for the dynamic structure
function in the whole experimentally accessible energy/momentum regime. Our
view is that the same physical effects -- namely fluctuations of the wave
function at an atomic length scale -- are responsible for the correct
energetics of the excitations in both Bose and Fermi fluids. Besides a
comprehensive derivation of the fermion version of the theory and discussion of
the approximations made, we present results for homogeneous He-3 and electrons
in three dimensions. We find indeed a significant lowering of the zero sound
mode in He-3 and a broadening of the collective mode due to the coupling to
particle-hole excitations in good agreement with experiments. The most visible
effect in electronic systems is the appearance of a ``double-plasmon''
excitation.Comment: submitted to Phys. Rev.
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