Non-Hermitian perturbative effective operators: Connectivity and derivation of diagrammatic representation

Effective Hamiltonians and effective operators act on a restricted model sp ace to give the same energies and matrix elements as those of the full Hami ltonian and operators between the corresponding true eigenstates. For the e ffective Hamiltonian there are two "obvious" choices: the simplest non-Herm itian effective Hamiltonian and the canonical Hermitian effective Hamiltoni an. In this paper, we derive a perturbative effective operator which works together with the non-Hermitian effective Hamiltonian, prove that it can be expanded with only connected diagrams, and show how to construct the conne cted diagrams easily from the diagrams of the effective Hamiltonian by subs titution of vertices. This effective operator is much simpler than the Herm itian effective operator and therefore is expected to be more suitable for ab initio calculations. (C) 2001 American Institute of Physics.