On the solution of the number-projected Hartree-Fock-Bogolyubov equations

Abstract

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble crankeddeformed shell model Hamiltonian. It is found that the solution of these number-projected equations involve similar numerical effort as that of bare HFB. We consider that this is a significant progress in the mean-field studies of the quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.

Formulation of functional theory for pairing with particle number restoration

“…The next the step will be the extension approach to perform variation after projection (VAP). VAP is usually solved using MR-EDF techniques by making variations with respect to the components of the original quasi-particle vacuum and not the projected state itself [20][21][22][23]. In the symmetry conserving approach, one could follow the same strategy as in the standard MR-EDF approach, i.e.…”

Projected quasiparticle theory for molecular electronic structure

“…The work that we here present builds upon the number projection formalism of Sheikh and Ring. [4][5][6] We expand and develop their technique to include many molecular symmetries not previously considered.…”

Strategies for extending geminal-based wavefunctions: Open shells and beyond

“…The edge-weights should capture the "linkedness" between the spin-orbitals: when two spin- (83) or the entanglement between the spin-orbitals. [120] Given the graph-theory representation of the links between orbitals, we can decide how to select the best permutations of orbitals.…”

“…In the subsequent sections of this paper, we will consider general strategies for extending Moreover, if one can restore the symmetry, then it is often possible to obtain even better results. [78][79][80][81][82][83][84][85][86][87][88][89] To understand this, expand a symmetry-broken wavefunction,  , as a linear combination of symmetry-labeled pieces  . We now consider the projected Schrödinger equation, and we will choose to project only on configuration state functions,…”