THE COUPLED-CLUSTER APPROACH TO QUANTUM MANY-BODY PROBLEM IN A THREE-HILBERT-SPACE REINTERPRETATION

Abstract

The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the groundstate wave functions |Ψ) = e^S |Φ) which live in the “physical” Hilbert space H^(P) using an elementary ansatz for |Φi plus a formal expansion of S in an operator basis of multi-configurational creation operators C⁺. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol H), which is self-adjoint in H^(P), to its effective lower-case isospectral avatar h = e^−SHe^S, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian h, which only appears manifestly non-Hermitian in its own (“friendly”) Hilbert space H^(F). This goal is achieved via an ad hoc amendment of the inner product in H^(F), thereby yielding the third (“standard”) Hilbert space H^(S). Due to the resulting exact unitary equivalence between the first and third spaces, H^(F) ∼ H^(S), the indistinguishability of predictions calculated in these alternative physical frameworks is guaranteed.