5,468 research outputs found
Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations
Molecular calculations in quantum Monte Carlo frequently employ a mixed basis
consisting of contracted and primitive Gaussian functions. While standard basis
sets of varying size and accuracy are available in the literature, we
demonstrate that reoptimizing the primitive function exponents within quantum
Monte Carlo yields more compact basis sets for a given accuracy. Particularly
large gains are achieved for highly excited states. For calculations requiring
non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that
behave as Gaussians at short distances and Slaters at long distances. These
basis functions further improve the energy and fluctuations of the local energy
for a given basis size. Gains achieved by exponent optimization and
Gauss-Slater basis use are exemplified by calculations for the ground state of
carbon, the lowest lying excited states of carbon with , ,
, symmetries, carbon dimer, and naphthalene. Basis size
reduction enables quantum Monte Carlo treatment of larger molecules at high
accuracy.Comment: 8 Pages, 2 Figures, 9 Table
Approaching Chemical Accuracy with Quantum Monte Carlo
A quantum Monte Carlo study of the atomization energies for the G2 set of
molecules is presented. Basis size dependence of diffusion Monte Carlo
atomization energies is studied with a single determinant Slater-Jastrow trial
wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the
mean absolute deviation from experimental atomization energies for the G2 set
is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo
improves the agreement between diffusion Monte Carlo and experiment, reducing
the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant
Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete
active space Slater-Jastrow trial wavefunction results in near chemical
accuracy. In this case, the mean absolute deviation from experimental
atomization energies is 1.2 kcal/mol. It is shown from calculations on systems
containing phosphorus that the accuracy can be further improved by employing a
larger active space.Comment: 6 pages, 5 figure
Assessing the performance of protective winter covers for outdoor marble statuary: pilot investigation
Outdoor statuary in gardens and parks in temperate climates has a tradition of being covered during the winter, to protect against external conditions. There has been little scientific study of the environmental protection that different types of covers provide. This paper examines environmental conditions provided by a range of covers used to protect marble statuary at three sites in the UK. The protection required depends upon the condition of the marble. Although statues closely wrapped and with a layer of insulation provide good protection, this needs to be considered against the potential physical damage of close wrapping a fragile deteriorated surface
Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick
model by means of the Holstein-Primakoff representation of the spin operators
and the continuous unitary transformations method. This combination allows us
to compute analytically leading corrections to the ground state energy, the
gap, the magnetization, and the two-spin correlation functions. We also present
numerical calculations for large system size which confirm the validity of this
approach. Finally, we use these results to discuss the entanglement properties
of the ground state focusing on the (rescaled) concurrence that we compute in
the thermodynamical limit.Comment: 20 pages, 9 figures, published versio
Finite-size scaling exponents and entanglement in the two-level BCS model
We analyze the finite-size properties of the two-level BCS model. Using the
continuous unitary transformation technique, we show that nontrivial scaling
exponents arise at the quantum critical point for various observables such as
the magnetization or the spin-spin correlation functions. We also discuss the
entanglement properties of the ground state through the concurrence which
appears to be singular at the transition.Comment: 4 pages, 3 figures, published versio
Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion
We describe a new data format for storing triangular, symmetric, and
Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard
two dimensional arrays of Fortran and C (also known as full format) that are
used to represent triangular and symmetric matrices waste nearly half of the
storage space but provide high performance via the use of Level 3 BLAS.
Standard packed format arrays fully utilize storage (array space) but provide
low performance as there is no Level 3 packed BLAS. We combine the good
features of packed and full storage using RFPF to obtain high performance via
using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF
requires exactly the same minimal storage as packed format. Each LAPACK full
and/or packed triangular, symmetric, and Hermitian routine becomes a single new
RFPF routine based on eight possible data layouts of RFPF. This new RFPF
routine usually consists of two calls to the corresponding LAPACK full format
routine and two calls to Level 3 BLAS routines. This means {\it no} new
software is required. As examples, we present LAPACK routines for Cholesky
factorization, Cholesky solution and Cholesky inverse computation in RFPF to
illustrate this new work and to describe its performance on several commonly
used computer platforms. Performance of LAPACK full routines using RFPF versus
LAPACK full routines using standard format for both serial and SMP parallel
processing is about the same while using half the storage. Performance gains
are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP
parallel times faster using vendor LAPACK full routines with RFPF than with
using vendor and/or reference packed routines
Similar glassy features in the NMR response of pure and disordered La1.88Sr0.12CuO4
High Tc superconductivity in La2-xSrxCuO4 coexists with (striped and glassy)
magnetic order. Here, we report NMR measurements of the 139La spin-lattice
relaxation, which displays a stretched-exponential time dependence, in both
pure and disordered x=0.12 single crystals. An analysis in terms of a
distribution of relaxation rates T1^-1 indicates that i) the spin-freezing
temperature is spatially inhomogeneous with an onset at Tg(onset)=20 K for the
pristine samples, and ii) the width of the T1^-1 distribution in the vicinity
of Tg(onset) is insensitive to an ~1% level of atomic disorder in CuO2 planes.
This suggests that the stretched-exponential 139La relaxation, considered as a
manifestation of the systems glassiness, may not arise from quenched disorder.Comment: 7 pages, to be published in Phys. Rev.
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