327 research outputs found
Systematic reduction of sign errors in many-body calculations of atoms and molecules
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf
79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an
accurate and robust method for calculating the ground state of atoms and
molecules. By direct comparison with accurate configuration interaction results
for the oxygen atom we show that SHDMC converges systematically towards the
ground-state wave function. We present results for the challenging N
molecule, where the binding energies obtained via both energy minimization and
SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that
SHDMC is robust enough to find the nodal surface for systems at least as large
as C starting from random coefficients. SHDMC is a linear-scaling
method, in the degrees of freedom of the nodes, that systematically reduces the
fermion sign problem.Comment: Final version accepted in Physical Review Letters. The review history
(referees' comments and our replies) is included in the source
Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks
We study the electronic structure of a spherical jellium in the presence of a
central Gaussian impurity. We test how well the resulting inhomogeneity effects
beyond spherical jellium are reproduced by several approximations of density
functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals,
namely local density approximation (LDA), generalized gradient approximation
(GGA), meta-GGA and orbital-dependent hybrid functionals are compared against
our quantum Monte Carlo (QMC) benchmarks. We identify several distinct
transitions in the ground state of the system as the electronic occupation
changes between delocalized and localized states. We examine the parameter
space of realistic densities () and moderate depths of the
Gaussian impurity (). The selected 18 electron system (with closed-shell
ground state) presents transitions while the 30 electron system
(with open-shell ground state) exhibits transitions. For the former
system, the accuracy for the transitions is clearly improving with increasing
sophistication of functionals with meta-GGA and hybrid functionals having only
small deviations from QMC. However, for the latter system, we find much larger
differences for the underlying transitions between our pool of DFT functionals
and QMC. We attribute this failure to treatment of the exact exchange within
these functionals. Additionally, we amplify the inhomogeneity effects by
creating the system with spherical shell which leads to even larger errors in
DFT approximations.Comment: 8 pages, 4 figures, submitted to PRB as a regular article revisited
version after revie
Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
Evaluation of pfaffians arises in a number of physics applications, and for
some of them a direct method is preferable to using the determinantal formula.
We discuss two methods for the numerical evaluation of pfaffians. The first is
tridiagonalization based on Householder transformations. The main advantage of
this method is its numerical stability that makes unnecessary the
implementation of a pivoting strategy. The second method considered is based on
Aitken's block diagonalization formula. It yields to a kind of LU (similar to
Cholesky's factorization) decomposition (under congruence) of arbitrary
skew-symmetric matrices that is well suited both for the numeric and symbolic
evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90)
implementing both methods are given. We also provide simple implementations in
Python and Mathematica for purpose of testing, or for exploratory studies of
methods that make use of pfaffians.Comment: 13 pages, Download links:
http://gamma.ft.uam.es/robledo/Downloads.html and
http://www.phys.washington.edu/users/bertsch/computer.htm
Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
We investigate the accuracy of trial wave function for quantum Monte Carlo
based on pfaffian functional form with singlet and triplet pairing. Using a set
of first row atoms and molecules we find that these wave functions provide very
consistent and systematic behavior in recovering the correlation energies on
the level of 95%. In order to get beyond this limit we explore the
possibilities of multi-pfaffian pairing wave functions. We show that a small
number of pfaffians recovers another large fraction of the missing correlation
energy comparable to the larger-scale configuration interaction wave functions.
We also find that pfaffians lead to substantial improvements in fermion nodes
when compared to Hartree-Fock wave functions.Comment: 4 pages, 2 figures, 2 tables, submitted to PR
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