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 s...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.展开更多
基金Supported by the National Natural Science Foundation of China(11405109)。
文摘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.
