The left-unitary operators that introduce the correlations of the hard core in an uncorrelated bound-state wave function of a finite number $A$ of particles are explicitly determined up to a unitary transformation. Left unitarity is required in order to keep orthonormality. Using a shell-model basis, transformed according to the correlation operator, it is possible to diagonalize the Hamiltonian in a subspace of the full Hilbert space with the technique of Bloch and Horowitz. Ground as well as excited states are treated on the same footing. In practice, the diagonalization is accomplished using the original single-particle basis and transforming back the Hamiltonian. This results in an $A$ -body operator for which a cluster expansion is possible. In this cluster expansion, there are three- and four-body terms easy to evaluate, because they factorize. A particularly interesting application can be made to few-body systems, evaluating the integrals numerically. The unique approximation is then connected with the cut of the basis. The method developed seems comparatively simple and is free of the mathematical problems of the hard core.The left-unitary operators that introduce the correlations of the hard core in an uncorrelated bound-state wave function of a finite number $A$ of particles are explicitly determined up to a unitary transformation. Left unitarity is required in order to keep orthonormality. Using a shell-model basis, transformed according to the correlation operator, it is possible to diagonalize the Hamiltonian in a subspace of the full Hilbert space with the technique of Bloch and Horowitz. Ground as well as excited states are treated on the same footing. In practice, the diagonalization is accomplished using the original single-particle basis and transforming back the Hamiltonian. This results in an $A$-body operator for which a cluster expansion is possible. In this cluster expansion, there are three- and four-body terms easy to evaluate, because they factorize. A particularly interesting application can be made to few-body systems, evaluating the integrals numerically. The unique approximation is then connected with the cut of the basis. The method developed seems comparatively simple and is free of the mathematical problems of the hard core.

Physical Review CJan 1, 19706 citations

Excitation Energies from the Entanglement Coupled Cluster Model for Doublets

Sarai Dery Folkestad, Kristine Lauvstad Kruken, Henrik Koch A

We present a spin-adapted coupled cluster singles and doubles model for the excitation energies of molecular doublets. The entanglement coupled cluster approach represents an unconventional take on the notorious problem of spin adaptation for open-shell species. In this approach, the high-spin open-shell molecular system is coupled to non-interacting bath orbitals to form a total closed-shell system. In entanglement coupled cluster theory, many of the attractive features of the spin-adapted closed-shell coupled cluster are retained: an unambiguous definition of the cluster operator and a terminating Baker-Campbell-Hausdorff expansion. The model produces excitation energies of a quality comparable to that of the closed-shell counterpart. Additionally, some ionized states that cannot be modeled accurately with the alternative equation-of-motion approach for ionized states can be described with the entanglement coupled cluster singles and doubles model.We present a spin-adapted coupled cluster singles and doubles model for the excitation energies of molecular doublets. The entanglement coupled cluster approach represents an unconventional take on the notorious problem of spin adaptation for open-shell species. In this approach, the high-spin open-shell molecular system is coupled to non-interacting bath orbitals to form a total closed-shell system. In entanglement coupled cluster theory, many of the attractive features of the spin-adapted closed-shell coupled cluster are retained: an unambiguous definition of the cluster operator and a terminating Baker-Campbell-Hausdorff expansion. The model produces excitation energies of a quality comparable to that of the closed-shell counterpart. Additionally, some ionized states that cannot be modeled accurately with the alternative equation-of-motion approach for ionized states can be described with the entanglement coupled cluster singles and doubles model.

arXiv:2504.04459The Journal of Physical Chemistry AJul 21, 20251 citation

New method of computing correlation functions. I

Raoul Rashidovich Nigmatullin

Russian Physics JournalOct 1, 19770 citations

New many-body method using cluster expansion diagrams with tensor-optimized antisymmetrized molecular dynamics

Takayuki Myo, Mengjiao Lyu, Hiroshi Toki +5 more

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$ -shell nuclei within the triple products of the correlation functions of tensor and central types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provide the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provide the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.

arXiv:2201.11877Physical Review CJan 21, 20226 citations

The left-unitary operators that introduce the correlations of the hard core in an uncorrelated bound-state wave function of a finite number

A

of particles are explicitly determined up to a unitary transformation. Left unitarity is required in order to keep orthonormality. Using a shell-model basis, transformed according to the correlation operator, it is possible to diagonalize the Hamiltonian in a subspace of the full Hilbert space with the technique of Bloch and Horowitz. Ground as well as excited states are treated on the same footing. In practice, the diagonalization is accomplished using the original single-particle basis and transforming back the Hamiltonian. This results in an

A

-body operator for which a cluster expansion is possible. In this cluster expansion, there are three- and four-body terms easy to evaluate, because they factorize. A particularly interesting application can be made to few-body systems, evaluating the integrals numerically. The unique approximation is then connected with the cut of the basis. The method developed seems comparatively simple and is free of the mathematical problems of the hard core.

s

-shell nuclei within the triple products of the correlation functions of tensor and central types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provide the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations.