186 research outputs found
Systematic reduction of sign errors in many-body problems: generalization of self-healing diffusion Monte Carlo to excited states
A recently developed self-healing diffusion Monte Carlo algorithm
[PRB 79, 195117] is extended to the calculation of excited states. The
formalism is based on an excited-state fixed-node approximation and the mixed
estimator of the excited-state probability density. The fixed-node ground state
wave-functions of inequivalent nodal pockets are found simultaneously using a
recursive approach. The decay of the wave-function into lower energy states is
prevented using two methods: i) The projection of the improved trial-wave
function into previously calculated eigenstates is removed. ii) The reference
energy for each nodal pocket is adjusted in order to create a kink in the
global fixed-node wave-function which, when locally smoothed out, increases the
volume of the higher energy pockets at the expense of the lower energy ones
until the energies of every pocket become equal. This reference energy method
is designed to find nodal structures that are local minima for arbitrary
fluctuations of the nodes within a given nodal topology. We demonstrate in a
model system that the algorithm converges to many-body eigenstates in
bosonic-like and fermionic cases.Comment: New version with two new figures. Several formulas of intermediate
steps in the analytical derivations have been added. The review reports and
replies with a summary of changes are included in the source pdf files with
nicer figures are also included in the sourc
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
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