243 research outputs found
Auxiliary-field quantum Monte Carlo study of first- and second-row post-d elements
A series of calculations for the first- and second-row post-d elements (Ga-Br
and In-I) are presented using the phaseless auxiliary-field quantum Monte Carlo
(AF QMC) method. This method is formulated in a Hilbert space defined by any
chosen one-particle basis, and maps the many-body problem into a linear
combination of independent-particle solutions with external auxiliary fields.
The phase/sign problem is handled approximately by the phaseless formalism
using a trial wave function, which in our calculations was chosen to be the
Hartree-Fock solution. We used the consistent correlated basis sets of Peterson
and coworkers, which employ a small core relativistic pseudopotential. The AF
QMC results are compared with experiment and with those from density-functional
(GGA and B3LYP) and coupled-cluster CCSD(T) calculations. The AF QMC total
energies agree with CCSD(T) to within a few milli-hartrees across the systems
and over several basis sets. The calculated atomic electron affinities,
ionization energies, and spectroscopic properties of dimers are, at large basis
sets, in excellent agreement with experiment.Comment: 10 pages, 2 figures. To be published in Journal of Chemical Physic
Bond breaking with auxiliary-field quantum Monte Carlo
Bond stretching mimics different levels of electron correlation and provides
a challenging testbed for approximate many-body computational methods. Using
the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC)
method, we examine bond stretching in the well-studied molecules BH and N,
and in the H chain. To control the sign/phase problem, the phaseless AF
QMC method constrains the paths in the auxiliary-field path integrals with an
approximate phase condition that depends on a trial wave function. With single
Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave
function, the phaseless AF QMC method generally gives better overall accuracy
and a more uniform behavior than the coupled cluster CCSD(T) method in mapping
the potential-energy curve. In both BH and N, we also study the use of
multiple-determinant trial wave functions from multi-configuration
self-consistent-field (MCSCF) calculations. The increase in computational cost
versus the gain in statistical and systematic accuracy are examined. With such
trial wave functions, excellent results are obtained across the entire region
between equilibrium and the dissociation limit.Comment: 8 pages, 3 figures and 3 tables. Submitted to JC
Eliminating spin contamination in auxiliary-field quantum Monte Carlo: realistic potential energy curve of F2
The use of an approximate reference state wave function |Phi_r> in electronic
many-body methods can break the spin symmetry of Born-Oppenheimer
spin-independent Hamiltonians. This can result in significant errors,
especially when bonds are stretched or broken. A simple spin-projection method
is introduced for auxiliary-field quantum Monte Carlo (AFQMC) calculations,
which yields spin-contamination-free results, even with a spin-contaminated
|Phi_r>. The method is applied to the difficult F2 molecule, which is unbound
within unrestricted Hartree-Fock (UHF). With a UHF |Phi_r>, spin contamination
causes large systematic errors and long equilibration times in AFQMC in the
intermediate, bond-breaking region. The spin-projection method eliminates these
problems, and delivers an accurate potential energy curve from equilibrium to
the dissociation limit using the UHF |Phi_r>. Realistic potential energy curves
are obtained with a cc-pVQZ basis. The calculated spectroscopic constants are
in excellent agreement with experiment.Comment: 8 pages, 6 figures, submitted to J. Chem. Phy
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
We extend the recently introduced phaseless auxiliary-field quantum Monte
Carlo (QMC) approach to any single-particle basis, and apply it to molecular
systems with Gaussian basis sets. QMC methods in general scale favorably with
system size, as a low power. A QMC approach with auxiliary fields in principle
allows an exact solution of the Schrodinger equation in the chosen basis.
However, the well-known sign/phase problem causes the statistical noise to
increase exponentially. The phaseless method controls this problem by
constraining the paths in the auxiliary-field path integrals with an
approximate phase condition that depends on a trial wave function. In the
present calculations, the trial wave function is a single Slater determinant
from a Hartree-Fock calculation. The calculated all-electron total energies
show typical systematic errors of no more than a few milli-Hartrees compared to
exact results. At equilibrium geometries in the molecules we studied, this
accuracy is roughly comparable to that of coupled-cluster with single and
double excitations and with non-iterative triples, CCSD(T). For stretched bonds
in HO, our method exhibits better overall accuracy and a more uniform
behavior than CCSD(T).Comment: 11 pages, 5 figures. submitted to JC
Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model
We simulated the 3-band Hubbard model using the Constrained Path Monte Carlo
(CPMC) method in search for a possible superconducting ground state. The CPMC
is a ground state method which is free of the exponential scaling of computing
time with system size. We calculated the binding energy of a pair of holes for
systems up to unit cells. We also studied the pairing correlation
functions versus distance for both the d-wave and extended s-wave channels in
systems up to . We found that holes bind for a wide range of
parameters and that the binding increased as the system size is increased.
However, the pairing correlation functions decay quickly with distance.
For the extended s channel, we found that as the Coulomb interaction on
the Cu sites is increased, the long-range part of the correlation functions is
suppressed and fluctuates around zero. For the channel, we
found that the correlations decay rapidly with distance towards a small
positive value. However, this value becomes smaller as the interaction or
the system size is increased.Comment: 21 pages, 13 Postscript figures, Submitted to Phys. Rev.
d-Wave Pairing Correlation in the Two-Dimensional t-J Model
The pair-pair correlation function of the two-dimensional t-J model is
studied by using the power-Lanczos method and an assumption of monotonic
behavior. In comparison with the results of the ideal Fermi gas, we conclude
that the 2D t-J model does not have long range d-wave superconducting
correlation in the interesting parameter range of . Implications
of this result will also be discussed.Comment: 4 pages, 6 figures, accepted by PR
Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model
The ground states of the two-dimensional repulsive Hubbard model are studied
within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge
properties are determined by systematic, large-scale, exact numerical
calculations, and quantified as a function of electron doping . In the
solution of the self-consistent UHF equations, multiple initial configurations
and simulated annealing are used to facilitate convergence to the global
minimum. New approaches are employed to minimize finite-size effects in order
to reach the thermodynamic limit. At low to moderate interacting strengths and
low doping, the UHF ground state is a linear spin-density wave (l-SDW), with
antiferromagnetic order and a modulating wave. The wavelength of the modulating
wave is . Corresponding charge order exists but is substantially weaker
than the spin order, hence holes are mobile. As the interaction is increased,
the l-SDW states evolves into several different phases, with the holes
eventually becoming localized. A simple pairing model is presented with
analytic calculations for low interaction strength and small doping, to help
understand the numerical results and provide a physical picture for the
properties of the SDW ground state. By comparison with recent many-body
calculations, it is shown that, for intermediate interactions, the UHF solution
provides a good description of the magnetic correlations in the true ground
state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table
A Constrained Path Monte Carlo Method for Fermion Ground States
We describe and discuss a recently proposed quantum Monte Carlo algorithm to
compute the ground-state properties of various systems of interacting fermions.
In this method, the ground state is projected from an initial wave function by
a branching random walk in an over-complete basis of Slater determinants. By
constraining the determinants according to a trial wave function
, we remove the exponential decay of signal-to-noise ratio
characteristic of the sign problem. The method is variational and is exact if
is exact. We illustrate the method by describing in detail its
implementation for the two-dimensional one-band Hubbard model. We show results
for lattice sizes up to and for various electron fillings and
interaction strengths. Besides highly accurate estimates of the ground-state
energy, we find that the method also yields reliable estimates of other
ground-state observables, such as superconducting pairing correlation
functions. We conclude by discussing possible extensions of the algorithm.Comment: 29 pages, RevTex, 3 figures included; submitted to Phys. Rev.
Bunching Transitions on Vicinal Surfaces and Quantum N-mers
We study vicinal crystal surfaces with the terrace-step-kink model on a
discrete lattice. Including both a short-ranged attractive interaction and a
long-ranged repulsive interaction arising from elastic forces, we discover a
series of phases in which steps coalesce into bunches of n steps each. The
value of n varies with temperature and the ratio of short to long range
interaction strengths. We propose that the bunch phases have been observed in
very recent experiments on Si surfaces. Within the context of a mapping of the
model to a system of bosons on a 1D lattice, the bunch phases appear as quantum
n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let
A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
We present the algorithmic details of the dynamical cluster approximation
(DCA), with a quantum Monte Carlo (QMC) method used to solve the effective
cluster problem. The DCA is a fully-causal approach which systematically
restores non-local correlations to the dynamical mean field approximation
(DMFA) while preserving the lattice symmetries. The DCA becomes exact for an
infinite cluster size, while reducing to the DMFA for a cluster size of unity.
We present a generalization of the Hirsch-Fye QMC algorithm for the solution of
the embedded cluster problem. We use the two-dimensional Hubbard model to
illustrate the performance of the DCA technique. At half-filling, we show that
the DCA drives the spurious finite-temperature antiferromagnetic transition
found in the DMFA slowly towards zero temperature as the cluster size
increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that
there is a finite temperature metal to insulator transition which persists into
the weak-coupling regime. This suggests that the magnetism of the model is
Heisenberg like for all non-zero interactions. Away from half-filling, we find
that the sign problem that arises in QMC simulations is significantly less
severe in the context of DCA. Hence, we were able to obtain good statistics for
small clusters. For these clusters, the DCA results show evidence of non-Fermi
liquid behavior and superconductivity near half-filling.Comment: 25 pages, 15 figure
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