Extending the VDPC+BCS formalism by including three-body forces* *Supported by the National Natural Science Foundation of China (11405109)

Abstract

Recently, Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian. The present study extends this formalism by including three-body forces. The result is the same as the so-called variation after particle-number projection in the BCS case, but now, the particle number is always conserved, and the time-consuming projection is avoided. Specifically, analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure. Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum. The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian. The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces. The average energy can be minimized to practically any arbitrary precision.