Pfaffian pairing and backflow wave functions for electronic structure quantum Monte Carlo methods

• Main Authors: Bajdich, M, Mitas, L, Wagner, L. K, Schmidt, K. E
• Format: Journal Article
• Language: English
• Published: 30-10-2006
• Subjects: Physics - Other Condensed Matter; Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.cond-mat/0610850

We investigate pfaffian trial wave functions with singlet and triplet pair
orbitals by quantum Monte Carlo methods. We present mathematical identities and
the key algebraic properties necessary for efficient evaluation of pfaffians.
Following upon our previous study \cite{pfaffianprl}, we explore the
possibilities of expanding the wave function in linear combinations of
pfaffians. We observe that molecular systems require much larger expansions
than atomic systems and linear combinations of a few pfaffians lead to rather
small gains in correlation energy. We also test the wave function based on
fully-antisymmetrized product of independent pair orbitals. Despite its
seemingly large variational potential, we do not observe additional gains in
correlation energy. We find that pfaffians lead to substantial improvements in
fermion nodes when compared to Hartree-Fock wave functions and exhibit the
minimal number of two nodal domains in agreement with recent results on fermion
nodes topology. We analyze the nodal structure differences of Hartree-Fock,
pfaffian and essentially exact large-scale configuration interaction wave
functions. Finally, we combine the recently proposed form of backflow
correlations \cite{drummond_bf,rios_bf} with both determinantal and pfaffian
based wave functions.