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The quantum many-body bound-state problem in its computationally successfulcoupled cluster method (CCM) representation is reconsidered. In conventionalpractice one factorizes the ground-state wave functions $|\Psi\rangle= e^S|\Phi\rangle$ which live in the "physical" Hilbert space ${\cal H}^{(P)}$ usingan elementary ansatz for $|\Phi\rangle$ plus a formal expansion of $S$ in anoperator basis of multi-configurational creation operators. In our paper areinterpretation of the method is proposed. Using parallels between the CCM andthe so called quasi-Hermitian, alias three-Hilbert-space (THS), quantummechanics, the CCM transition from the known microscopic Hamiltonian (denotedby usual symbol $H$), which is self-adjoint in ${\cal H}^{(P)}$, to itseffective lower-case isospectral avatar $\hat{h}=e^{-S} H e^S$, is assigned aTHS interpretation. In the opposite direction, a THS-prescribed, non-CCM,innovative reinstallation of Hermiticity is shown to be possible for the CCMeffective Hamiltonian $\hat{h}$, which only appears manifestly non-Hermitian inits own ("friendly") Hilbert space ${\cal H}^{(F)}$. This goal is achieved viaan ad hoc amendment of the inner product in ${\cal H}^{(F)}$, thereby yieldingthe third ("standard") Hilbert space ${\cal H}^{(S)}$. Due to the resultingexact unitary equivalence between the first and third spaces, ${\calH}^{(P)}\sim {\cal H}^{(S)}$, the indistinguishability of predictionscalculated in these alternative physical frameworks is guaranteed.

The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation