Condensed Matter Seminar Series

Topology of Fermion Nodes and Pfaffian Pairing Wavefunctions

Lubos Mitas*

NC State University

Thursday October 19,  11:30 am,  Room 298,  Physics Building

Abstract:  We show that under rather general conditions closed-shell ground state wavefunctions of fermionic systems in d>1 have two nodal domains for arbitrary system size. The explicit proofs cover paradigmatic models such as
fermions on a sphere surface, in a periodic box, atomic states, etc,  and are based on algebraic arguments and  BCS variational wavefunctions  [1,2]. The correct nodal topology is of a key importance for quantum Monte Carlo fixed-node methods, and for this purpose we propose a new wavefunction which includes both singlet and triplet pairing functions inside a pfaffian [3]. Using a testing set of first row atoms and molecules, we show that wavefunctions based on pfaffians are comparable to much larger configuration interaction expansions. For small systems we compare Hartree-Fock, pfaffian, and essentially exact wavefunctions and analyze the structure of corresponding nodal manifolds. 

* in collaboration with L.K. Wagner, M. Bajdich, G. Drobny, K.E Schmidt (Arizona State U.).

[1] L. Mitas, PRL 96, 240402 (2006)
[2] L. Mitas, cond-mat/0605550.
[3] M. Bajdich, L.K. Wagner, G. Drobny, L. Mitas, K. E. Schmidt, PRL 96,130201 (2006)