On January 19, 2010 Lubos Mitas (North Carolina State University) will be delivering a lecture entitled “Quantum Monte Carlo: many-body effects, fermion nodes and pfaffians “.

Location: 2237 French Family Science Center

Time: 4:30pm

Abstract: Quantum Monte Carlo (QMC) methods map quantum many-body problems onto simulations of multi-dimensional stochastic processes. Although QMC algorithms suffer from the well-known fermion or other sign problems, in continuous space the signs can be eliminated by introducing boundaries specified by the nodal hypersurfaces (wave function zero sets). Interestingly, even rather crude mean-field nodes enable to achieve remarkably accurate insights and predictions for systems with hundreds of particles. For example, solutions of the electrons-ions stationary Schrodinger equation by the fixed-node QMC yield 90-95% of many-body correlations. Reaching beyond this fixed-node accuracy limit, though, requires much better understanding of the node’s properties, such as nodal domain topologies, nodel shapes, etc. Recently, we have proved that noninteracting and mean-field models in d>1 have fermionic ground states with the minimal number of two nodal domains for any system size. For interacting fermions we have shown that wave functions based on pair orbitals have the necessary variational freedom to describe the correct nodal topologies. We have proposed and tested pfaffian wave functions with both singlet and triplet pair orbitals as an elegant and easy to evaluate form for practical calculations. Further recent results and applications of these ideas will be discussed.