Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods

Abstract

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, 1 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 2,3 with both determinantal and pfaffian based wave functions.

Using CIPSI Nodes in Diffusion Monte Carlo

“…Results for canonical and natural orbitals are given. [72][73][74][75][76][77][78][79]). However, the most popular one is certainly the Jastrow-Slater trial wavefunction expressed as a short expansion over a set of Slater determinants multiplied by a global Jastrow factor describing explicitly the electron-electron and electron-electron-nucleus interactions and, in particular, imposing the electron-electron cusp conditions associated with the zero-interelectronic distance limit of the true wavefunction.…”

Paired chiral spin liquid with a Fermi surface inS=1model on the triangular lattice

“…4 For the QSL states with equal-flavor pairing (fwave, p+ip), the wave function is a product of three Pfaffians, 60,61 …”

“…59 This allows for efficient evaluation of determinants and Pfaffians with rows and/or columns replaced or removed. 22,61,62 To update the inverse of an anti-symmetric matrix with a row and column replaced, we use the Sherman-Morrison algorithm 63 twice, followed by anti-symmetrization of the matrix. This procedure greatly improves the numerical stability of the update.…”

Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

“…Introduced fixed-node errors can be reduced by expanding the trial wave function in multi-determinants 12,14 or by using the backflow correlation corrections [52][53][54][55] , or both. Previously, it was found that the QMC calculations for the closed shell jellium spheres 18 did not suffer from large fixed-node errors (by comparing to FN-DMC results with small multi-determinant expansions 17 ).…”