The unitary group and the particle hole concept

F.A. Matsen

Josef Paldus, M. J. Boyle

A hole-particle version of the unitary group approach to the many-electron correlation problem is given. To achieve a unique state labeling, the subgroup chain of Flores and Moshinsky for the nuclear many-body problem is modified, and the rules for the construction of relevant irreducible representations and of the orthonormal spinadapted states are given. The structure of these hole-particle formalism spin-adapted bases is illustrated on several examples for all the three possible types of the hole-particle defect pertaining to the excitation, electron attachment, or detachment processes relative to the reference state used. The tensor character of the particle formalism electron-number-preserving generators is pointed out, and their basic classification in the hole-particle formalism is given.

Hao Ran Gong, Xiao-Xia Ruan, Hong-Shi Zong

We calculate the pressure and entropy of a unitary Fermi gas based on universal relations combined with our previous prediction of energy which was calculated within the framework of the non-self-consistent T-matrix approximation with particle-hole fluctuation. The resulting entropy and pressure are compared with the experimental data and the theoretical results without induced interaction. For entropy, we find good agreement between our results with particle-hole fluctuation and the experimental measurements reported by ENS group and MIT experiment. For pressure, our results suffer from a systematic upshift compared to MIT data.

Isaiah Shavitt

Werner Kutzelnigg

A particle-hole formalism is defined which is consistent with the tensor notation (and the index pairing) of the generators of the unitary group and their many-particle generalization. The corresponding generalized Wick theorem is formulated. The classification of basis operators as ‘‘closed,’’ ‘‘open,’’ ‘‘closed from above,’’ and ‘‘closed from below’’ given previously is extended to the present context. Both the perturbative and nonperturbative construction of effective Fock space Hamiltonians is discussed in the particle-hole formalism, especially for the case that the ‘‘physical vacuum’’ satisfies a Hartree–Fock condition. For the calculations of the correlation energy of the physical vacuum Cizek’s CP-MET is compared formally with the unitary variant, the UNICEP (unitary coupled electron pair) approximation. A simple derivation of Goldstone’s ‘‘linked-cluster expansion’’ is also given.