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Alleviation of the Fermion-sign problem by optimization of many-body wave functions

C. J. Umrigar·Julien Toulouse·Claudia Filippi·S. Sorella·R. G. Hennig
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Abstract

We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wav e function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C$_2$ molecule to the experimental accuracy of 0.02 eV.

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C. J. Umrigar, Julien Toulouse, Claudia Filippi, S. Sorella, R. G. Hennig. 2006-11-08. Alleviation of the Fermion-sign problem by optimization of many-body wave functions. https://doi.org/10.1103/physrevlett.99.179902

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