Fermion nodes and pfaffian pairing wave functions: qauntum Monte Carlo beyond the fixed-node approximation

Lubos Mitas

North Carolina State University

------------------------------------------------------------------------ Structure of fermion nodes and nodal cells L. Mitas We study nodes of fermionic ground state wave functions. For $2D$ and higher we prove that spin-polarized, noninteracting fermions in a harmonic well have two nodal cells for arbitrary system size. The result extends to other noninteracting/mean-field models such as fermions on a sphere, in a periodic box or in Hartree-Fock atomic states. Spin-unpolarized noninteracting states have multiple nodal cells, however, interactions and many-body correlations generally relax the multiple cells to the minimal number of two. With some conditions, this is proved for interacting $2D$ and higher harmonic fermion systems of arbitrary size using the Bardeen-Cooper-Schrieffer variational wave function. ------------------------------------------------------------------------ Pfaffian pairing wave functions in electronic structure quantum Monte Carlo M. Bajdich, L. Mitas, G. Drobny, L. Wagner and K.E. Schmidt We investigate the limits of accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that this wave functions provide very consistent and systematic behaviour in recovering the correlation energies on the level of 95\% . In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that small number of pfaffians recovers another large fraction of the missing correlation energy up to 99\% comparable to the large-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wavefunctions. --------------------------------------------------------------------------