N-electron Slater determinants from non-unitary canonical transformations of fermion operators
Abstract
Mean-field methods such as Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB) constitute the building blocks upon which more elaborate many-body theories are based on. The HF and HFB wavefunctions are built out of independent quasi-particles resulting from a unitary linear canonical transformation of the elementary fermion operators. Here, we discuss the possibility of allowing the HF transformation to become non-unitary. The properties of such HF vacua are discussed, as well as the evaluation of matrix elements among such states. We use a simple ansatz to demonstrate that a non-unitary transformation brings additional flexibility that can be exploited in variational approximations to many-fermion wavefunctions. The action of projection operators on non-unitary based HF states is also discussed and applied to the one-dimensional Hubbard model with periodic boundary conditions.
Keywords
Cite
@article{arxiv.1208.0037,
title = {N-electron Slater determinants from non-unitary canonical transformations of fermion operators},
author = {Carlos A. Jimenez-Hoyos and R. Rodriguez-Guzman and Gustavo E. Scuseria},
journal= {arXiv preprint arXiv:1208.0037},
year = {2013}
}