Condensed-Matter Physics & Materials Science Seminar

Quantum Monte Carlo methods are capable of high-accuracy description of many-body effects in real or model quantum systems such as molecules, clusters, solids, BEC-BCS model systems, etc, often recovering 95% of correlation energy in systems with hundreds of quantum particles. For fermions in continuous space the major remaining barrier for improving upon this already remarkable performance is the so-called fixed-node approximation. The fermion nodes of many-body wavefunctions are notoriously difficult to improve and many of their properties, including nodal cell topologies and exact shapes, have been unknown. We explicitly prove that for d>1 the nondegenerate fermionic ground states have the minimal number of two nodal cells for any system size under rather general conditions. For systems with interactions the proof is based on exploring the properties of BCS wavefunctions. The same property is demonstrated for temperature density matrices in d>1. These proofs have inspired search for trial wavefunctions which demonstrably possess the correct nodal topologies. To this end, we have proposed and tested pfaffian wavefunctions with both singlet and triplet pairing orbitals in a single and easy to evaluate form as an efficient way to capture the correct topological properties. The recent results and applications of these ideas will be discussed.


REFERENCES
[1] PRL 96, 130201; PRL 96, 240402; cond-mat/0610088, /0605550.