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Coupled-cluster method in Fock space. I. General formalism

Physical Review A, ISSN: 1050-2947, Vol: 32, Issue: 2, Page: 725-742
1985
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The problem of finding the spectrum of the Fock-space Hamiltonian for a system of many fermions is analyzed. The quasiparticle formalism is employed, with holes and particles defined with respect to some N-particle determinantal wave function (the model vacuum). The basic idea behind the proposed approach is to perform a similarity transformation of Hamiltonian , such that the resulting effective Hamiltonian is, unlike , a quasiparticle-numberconserving operator. It is shown that eigenvalues of , corresponding to small numbers of quasiparticles (0,1,2) can be easily calculated. This is equivalent to finding eigenvalues of for certain states of N, N1, and N2 particles. The construction of the operator transforming into (the wave operator) stems from an analysis of the structure of the algebra of linear operators acting in a (finite-dimensional) Fock space. The exponential Ansatz for the wave operator is used, resulting in a generalization of the coupled-cluster (CC) method of Coester [Nucl. Phys. 7, 421 (1958)]. The generalized CC equations determining the wave operator, and equations determining the effective Hamiltonian , are presented in a diagrammatic form. An effort has been made to obtain a concise notation for expressing these equations in an algebraic form. Approximation schemes, necessary for practical applications of the proposed method, are also studied. © 1985 The American Physical Society.

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