325 research outputs found
Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions
We investigate Monte Carlo energy and variance minimization techniques for
optimizing many-body wave functions. Several variants of the basic techniques
are studied, including limiting the variations in the weighting factors which
arise in correlated sampling estimations of the energy and its variance. We
investigate the numerical stability of the techniques and identify two reasons
why variance minimization exhibits superior numerical stability to energy
minimization. The characteristics of each method are studied using a
non-interacting 64-electron model of crystalline silicon. While our main
interest is in solid state systems, the issues investigated are relevant to
Monte Carlo studies of atoms, molecules and solids. We identify a robust and
efficient variance minimization scheme for optimizing wave functions for large
systems.Comment: 14 pages, including 7 figures. To appear in Phys. Rev. B. For related
publications see http://www.tcm.phy.cam.ac.uk/Publications/many_body.htm
Hydrogen/silicon complexes in silicon from computational searches
Defects in crystalline silicon consisting of a silicon self-interstitial atom
and one, two, three, or four hydrogen atoms are studied within
density-functional theory (DFT). We search for low-energy defects by starting
from an ensemble of structures in which the atomic positions in the defect
region have been randomized. We then relax each structure to a minimum in the
energy. We find a new defect consisting of a self-interstitial and one hydrogen
atom (denoted by {I,H}) which has a higher symmetry and a lower energy than
previously reported structures. We recover the {I,H_2} defect found in previous
studies and confirm that it is the most stable such defect. Our best {I,H_3}
defect has a slightly different structure and lower energy than the one
previously reported, and our lowest energy {I,H_4} defect is different to those
of previous studies.Comment: 7 pages, 8 figure
A Geometric Formulation of Quantum Stress Fields
We present a derivation of the stress field for an interacting quantum system
within the framework of local density functional theory. The formulation is
geometric in nature and exploits the relationship between the strain tensor
field and Riemannian metric tensor field. Within this formulation, we
demonstrate that the stress field is unique up to a single ambiguous parameter.
The ambiguity is due to the non-unique dependence of the kinetic energy on the
metric tensor. To illustrate this formalism, we compute the pressure field for
two phases of solid molecular hydrogen. Furthermore, we demonstrate that
qualitative results obtained by interpreting the hydrogen pressure field are
not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper
supersedes cond-mat/000627
Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon
The band structure of silicon is calculated at the Gamma, X, and L wave
vectors using diffusion quantum Monte Carlo methods. Excited states are formed
by promoting an electron from the valence band into the conduction band. We
obtain good agreement with experiment for states around the gap region and
demonstrate that the method works equally well for direct and indirect
excitations, and that one can calculate many excited states at each wave
vector. This work establishes the fixed-node DMC approach as an accurate method
for calculating the energies of low lying excitations in solids.Comment: 5 pages, 1 figur
Elasticity of entangled polymer loops: Olympic gels
In this note we present a scaling theory for the elasticity of olympic gels,
i.e., gels where the elasticity is a consequence of topology only. It is shown
that two deformation regimes exist. The first is the non affine deformation
regime where the free energy scales linear with the deformation. In the large
(affine) deformation regime the free energy is shown to scale as where is the deformation ratio. Thus a highly non
Hookian stress - strain relation is predicted.Comment: latex, no figures, accepted in PRE Rapid Communicatio
Optical spectra and exchange-correlation effects in molecular crystals
We report first-principles GW-Bethe Salpeter Equation and Quantum Monte Carlo
calculations of the optical and electronic properties of molecular and
crystalline rubrene (CH). Many-body effects dominate the optical
spectrum and quasi-particle gap of molecular crystals. We interpret the
observed yellow-green photoluminescence in rubrene microcrystals as a result of
the formation of intermolecular, charge-transfer spin-singlet excitons. In
contrast, spin-triplet excitons are localized and intramolecular with a
predicted phosphorescence at the red end of the optical spectrum. We find that
the exchange energy plays a fundamental role in raising the energy of
intramolecular spin-singlet excitons above the intermolecular ones. Exciton
binding energies are predicted to be around 0.5 eV (spin singlet) to 1 eV (spin
triplet). The calculated electronic gap is 2.8 eV. The theoretical absorption
spectrum agrees very well with recent ellipsometry data.Comment: 4 pages, 4 figure
Excitons in T-shaped quantum wires
We calculate energies, oscillator strengths for radiative recombination, and
two-particle wave functions for the ground state exciton and around 100 excited
states in a T-shaped quantum wire. We include the single-particle potential and
the Coulomb interaction between the electron and hole on an equal footing, and
perform exact diagonalisation of the two-particle problem within a finite basis
set. We calculate spectra for all of the experimentally studied cases of
T-shaped wires including symmetric and asymmetric GaAs/AlGaAs and
InGaAs/AlGaAs structures. We study in detail the
shape of the wave functions to gain insight into the nature of the various
states for selected symmetric and asymmetric wires in which laser emission has
been experimentally observed. We also calculate the binding energy of the
ground state exciton and the confinement energy of the 1D quantum-wire-exciton
state with respect to the 2D quantum-well exciton for a wide range of
structures, varying the well width and the Al molar fraction . We find that
the largest binding energy of any wire constructed to date is 16.5 meV. We also
notice that in asymmetric structures, the confinement energy is enhanced with
respect to the symmetric forms with comparable parameters but the binding
energy of the exciton is then lower than in the symmetric structures. For
GaAs/AlGaAs wires we obtain an upper limit for the binding energy
of around 25 meV in a 10 {\AA} wide GaAs/AlAs structure which suggests that
other materials must be explored in order to achieve room temperature
applications. There are some indications that
InGaAs/AlGaAs might be a good candidate.Comment: 20 pages, 10 figures, uses RevTeX and psfig, submitted to Physical
Review
Interpolated wave functions for nonadiabatic simulations with the fixed-node quantum Monte Carlo method
Simulating nonadiabatic effects with many-body wave function approaches is an
open field with many challenges. Recent interest has been driven by new
algorithmic developments and improved theoretical understanding of properties
unique to electron-ion wave functions. Fixed-node diffusion Monte Caro is one
technique that has shown promising results for simulating electron-ion systems.
In particular, we focus on the CH molecule for which previous results suggested
a relatively significant contribution to the energy from nonadiabatic effects.
We propose a new wave function ansatz for diatomic systems which involves
interpolating the determinant coefficients calculated from configuration
interaction methods. We find this to be an improvement beyond previous wave
function forms that have been considered. The calculated nonadiabatic
contribution to the energy in the CH molecule is reduced compared to our
previous results, but still remains the largest among the molecules under
consideration.Comment: 7 pages, 3 figure
Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters
We report a first-principles theoretical study of hyperfine interactions,
zero-point effects and defect energetics of muonium and hydrogen impurities in
silicon and germanium. The spin-polarized density functional method is used,
with the crystalline orbitals expanded in all-electron Gaussian basis sets. The
behaviour of hydrogen and muonium impurities at both the tetrahedral and
bond-centred sites is investigated within a supercell approximation. To
describe the zero-point motion of the impurities, a double adiabatic
approximation is employed in which the electron, muon/proton and host lattice
degrees of freedom are decoupled. Within this approximation the relaxation of
the atoms of the host lattice may differ for the muon and proton, although in
practice the difference is found to be slight. With the inclusion of zero-point
motion the tetrahedral site is energetically preferred over the bond-centred
site in both silicon and germanium. The hyperfine and superhyperfine
parameters, calculated as averages over the motion of the muon, agree
reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.
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