8,725 research outputs found
A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
We present an efficient low-rank updating algorithm for updating the trial
wavefunctions used in Quantum Monte Carlo (QMC) simulations. The algorithm is
based on low-rank updating of the Slater determinants. In particular, the
computational complexity of the algorithm is O(kN) during the k-th step
compared with traditional algorithms that require O(N^2) computations, where N
is the system size. For single determinant trial wavefunctions the new
algorithm is faster than the traditional O(N^2) Sherman-Morrison algorithm for
up to O(N) updates. For multideterminant configuration-interaction type trial
wavefunctions of M+1 determinants, the new algorithm is significantly more
efficient, saving both O(MN^2) work and O(MN^2) storage. The algorithm enables
more accurate and significantly more efficient QMC calculations using
configuration interaction type wavefunctions
Density-density functionals and effective potentials in many-body electronic structure calculations
We demonstrate the existence of different density-density functionals
designed to retain selected properties of the many-body ground state in a
non-interacting solution starting from the standard density functional theory
ground state. We focus on diffusion quantum Monte Carlo applications that
require trial wave functions with optimal Fermion nodes. The theory is
extensible and can be used to understand current practices in several
electronic structure methods within a generalized density functional framework.
The theory justifies and stimulates the search of optimal empirical density
functionals and effective potentials for accurate calculations of the
properties of real materials, but also cautions on the limits of their
applicability. The concepts are tested and validated with a near-analytic
model.Comment: five figure
Pseudogap and antiferromagnetic correlations in the Hubbard model
Using the dynamical cluster approximation and quantum monte carlo we
calculate the single-particle spectra of the Hubbard model with next-nearest
neighbor hopping . In the underdoped region, we find that the pseudogap
along the zone diagonal in the electron doped systems is due to long range
antiferromagnetic correlations. The physics in the proximity of is
dramatically influenced by and determined by the short range correlations.
The effect of on the low energy ARPES spectra is weak except close to the
zone edge. The short range correlations are sufficient to yield a pseudogap
signal in the magnetic susceptibility, produce a concomitant gap in the
single-particle spectra near but not necessarily at a location in
the proximity of Fermi surface.Comment: 5 pages, 4 figure
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
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