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Journal of Physics and Chemistry of Solids

Systematic improvement of wavefunctions in the variational Monte Carlo method for the t–J model

Masanori Kohno, Masatoshi Imada

Published Jun 1, 2002• 1 citation
Publisher
DOI
10.1016/s0022-3697(02)00047-1

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We introduce an algorithm that can be used to perform stochastic perturbation theory (sPT) to correct any non-linearly parametrized wavefunction that can be optimized using orbital space Variational Monte Carlo (VMC). Although the variational method gaurantees that the VMC energy can be systematically improved the cost of doing so in practice is often prohibitive. The sPT algorithm presented in this work represents an efficient way to improve the VMC energies with a relatively small computational overhead. We demonstrate that for the carbon dimer and Fe-porphyrin the sPT algorithm is able to capture >97%>97\%>97% and >60%>60\%>60% respectively of the correlation energy missing from the zeroth order wavefunction. Further, the sPT algorithm is also ideally suited for massively parallel computations because it delivers super-linear speedup with an increasing number of processors.
While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced.