891 research outputs found
Lowering of the Kinetic Energy in Interacting Quantum Systems
Interactions never lower the ground state kinetic energy of a quantum system.
However, at nonzero temperature, where the system occupies a thermal
distribution of states, interactions can reduce the kinetic energy below the
noninteracting value. This can be demonstrated from a first order weak coupling
expansion. Simulations (both variational and restricted path integral Monte
Carlo) of the electron gas model and dense hydrogen confirm this and show that
in contrast to the ground state case, at nonzero temperature the population of
low momentum states can be increased relative to the free Fermi distribution.
This effect is not seen in simulations of liquid He-3.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett., June, 200
An Exact Monte Carlo Method for Continuum Fermion Systems
We offer a new proposal for the Monte Carlo treatment of many-fermion systems
in continuous space. It is based upon Diffusion Monte Carlo with significant
modifications: correlated pairs of random walkers that carry opposite signs;
different functions ``guide'' walkers of different signs; the Gaussians used
for members of a pair are correlated; walkers can cancel so as to conserve
their expected future contributions. We report results for free-fermion systems
and a fermion fluid with 14 He atoms, where it proves stable and correct.
Its computational complexity grows with particle number, but slowly enough to
make interesting physics within reach of contemporary computers.Comment: latex source, 3 separated figures (2 in jpg format, 1 in eps format
The Coupled Electronic-Ionic Monte Carlo Simulation Method
Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion
Monte Carlo or Path Integral Monte Carlo are the most accurate and general
methods for computing total electronic energies. We will review methods we have
developed to perform QMC for the electrons coupled to a classical Monte Carlo
simulation of the ions. In this method, one estimates the Born-Oppenheimer
energy E(Z) where Z represents the ionic degrees of freedom. That estimate of
the energy is used in a Metropolis simulation of the ionic degrees of freedom.
Important aspects of this method are how to deal with the noise, which QMC
method and which trial function to use, how to deal with generalized boundary
conditions on the wave function so as to reduce the finite size effects. We
discuss some advantages of the CEIMC method concerning how the quantum effects
of the ionic degrees of freedom can be included and how the boundary conditions
can be integrated over. Using these methods, we have performed simulations of
liquid H2 and metallic H on a parallel computer.Comment: 27 pages, 10 figure
Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
We justify a recently proposed prescription for performing Green Function
Monte Carlo calculations on systems of lattice fermions, by which one is able
to avoid the sign problem. We generalize the prescription such that it can also
be used for problems with hopping terms of different signs. We prove that the
effective Hamiltonian, used in this method, leads to an upper bound for the
ground-state energy of the real Hamiltonian, and we illustrate the
effectiveness of the method on small systems.Comment: 14 pages in revtex v3.0, no figure
Correlations in Hot Dense Helium
Hot dense helium is studied with first-principles computer simulations. By
combining path integral Monte Carlo and density functional molecular dynamics,
a large temperature and density interval ranging from 1000 to 1000000 K and 0.4
to 5.4 g/cc becomes accessible to first-principles simulations and the changes
in the structure of dense hot fluids can be investigated. The focus of this
article are pair correlation functions between nuclei, between electrons, and
between electrons and nuclei. The density and temperature dependence of these
correlation functions is analyzed in order to describe the structure of the
dense fluid helium at extreme conditions.Comment: accepted for publication in Journal of Physics
Quantum Monte Carlo study of a positron in an electron gas
Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects
Nuclear quantum effects in water
In this work, a path integral Car-Parrinello molecular dynamics simulation of
liquid water is performed. It is found that the inclusion of nuclear quantum
effects systematically improves the agreement of first principles simulations
of liquid water with experiment. In addition, the proton momentum distribution
is computed utilizing a recently developed open path integral molecular
dynamics methodology. It is shown that these results are in good agreement with
neutron Compton scattering data for liquid water and ice.Comment: 4 page
The Coupled Electron-Ion Monte Carlo Method
In these Lecture Notes we review the principles of the Coupled Electron-Ion
Monte Carlo methods and discuss some recent results on metallic hydrogen.Comment: 38 pages, 6 figures, Lecture notes for the International School of
Solid State Physics, 34th course: "Computer Simulation in Condensed Matter:
from Materials to Chemical Biology", 20 July-1 August 2005 Erice (Italy). To
appear in Lecture Notes in Physics (2006
Twist-averaged Boundary Conditions in Continuum Quantum Monte Carlo
We develop and test Quantum Monte Carlo algorithms which use a``twist'' or a
phase in the wave function for fermions in periodic boundary conditions. For
metallic systems, averaging over the twist results in faster convergence to the
thermodynamic limit than periodic boundary conditions for properties involving
the kinetic energy with the same computational complexity. We determine
exponents for the rate of convergence to the thermodynamic limit for the
components of the energy of coulomb systems. We show results with twist
averaged variational Monte Carlo on free particles, the Stoner model and the
electron gas using Hartree-Fock, Slater-Jastrow, three-body and backflow
wavefunction. We also discuss the use of twist averaging in the grand canonical
ensemble, and numerical methods to accomplish the twist averaging.Comment: 8 figures, 12 page
Single and Paired Point Defects in a 2D Wigner Crystal
Using the path-integral Monte Carlo method, we calculate the energy to form
single and pair vacancies and interstitials in a two-dimensional Wigner crystal
of electrons. We confirm that the lowest-lying energy defects of a 2D electron
Wigner crystal are interstitials, with a creation energy roughly 2/3 that of a
vacancy. The formation energy of the defects goes to zero near melting,
suggesting that point defects might mediate the melting process. In addition,
we find that the interaction between defects is strongly attractive, so that
most defects will exist as bound pairs.Comment: 4 pages, 5 encapsulated figure
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