SCIENCE
Users develop pfaffian approach to describing many-body quantum systems
Wave functions of interacting quantum systems such as electrons in matter are notoriously difficult to calculate despite decades of effort. One of the most productive many-body methods for electronic structure problems is quantum Monte Carlo. QMC has been very successful for a host of real systems such as molecules, clusters, and solids with up to hundreds of valence electrons. 
In April 2006, North Carolina State University's Lubos Mitas and a team from NC State and Arizona State University proposed a new functional form for the efficient description of many-body quantum systems using QMC. This method was published in Physical Review Letters and developed on NCSA's Tungsten and Copper clusters. The team also computed at NCSA's sister sites, the Pittsburgh Supercomputing Center and the San Diego Supercomputer Center.
The team's new method is based on what is called Pfaffian, a mathematical approach to solving skew-symmetric matrices. It allows users to incorporate pair orbitals for both singlet and triplet pairing channels with unpaired one-particle orbitals into a single, compact wave function. With singlet pairing, the correlation between unlike-spin electrons can be described. Triplet pairing does the same for same-spin electron pairs.
Pfaffian wave functions capture the same effects as conventional methods of solving, which are an order of magnitude or more expensive to calculate. The team has alos found that Pfaffian wave functions lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.
In April 2006, North Carolina State University's Lubos Mitas and a team from NC State and Arizona State University proposed a new functional form for the efficient description of many-body quantum systems using QMC. This method was published in Physical Review Letters and developed on NCSA's Tungsten and Copper clusters. The team also computed at NCSA's sister sites, the Pittsburgh Supercomputing Center and the San Diego Supercomputer Center.
The team's new method is based on what is called Pfaffian, a mathematical approach to solving skew-symmetric matrices. It allows users to incorporate pair orbitals for both singlet and triplet pairing channels with unpaired one-particle orbitals into a single, compact wave function. With singlet pairing, the correlation between unlike-spin electrons can be described. Triplet pairing does the same for same-spin electron pairs.
Pfaffian wave functions capture the same effects as conventional methods of solving, which are an order of magnitude or more expensive to calculate. The team has alos found that Pfaffian wave functions lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions. 