N-electron Slater determinants from non-unitary canonical transformations of fermion operators

TL;DR

This paper explores non-unitary canonical transformations in Hartree-Fock methods, offering increased flexibility for variational approximations of many-fermion wavefunctions, and demonstrates their application to the Hubbard model.

Contribution

It introduces non-unitary transformations in Hartree-Fock theory, expanding the variational space for better many-fermion wavefunction approximations.

Findings

Non-unitary transformations provide additional variational flexibility.

Application to the 1D Hubbard model shows potential improvements.

Matrix elements can be evaluated for non-unitary HF states.

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.