Microscopic theory of particle-hole states

M. -C. Bouten, Piet Van Leuven, Miodrag V. Mihailović +1 more

Lu Jia

The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work I show that this symmetry is preserved in the subspace truncated up to a certain generalized seniority and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, I study particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and other models.

Rosina, M.

Ajit Coimbatore Balram, Jainendra K. Jain

Motivated by the particle-hole symmetry at the half-filled lowest Landau level, many articles have taken the point of view, following D. T. Son, that composite fermions are Dirac particles and their Fermi sea is akin to that occurring at the surface of a three dimensional topological insulator. This presents a paradox, because the microscopic theory of composite fermions, which treats composite fermions as non-relativistic particles, has been confirmed in great detail. The authors discuss what features of the Dirac-composite fermion view can be reconciled with the microscopic theory. They also show how particle-hole symmetry can emerge in the Chern-Simons formulation of composite fermions.

Abraham Klein, Tsutomu Une

In an accompanying paper, we have described a new approach to the computation of ground-state energies and of correlated particle-hole excitations in terms of a phenomenological pseudo-Hamiltonian containing two- and more-body smooth effective potentials which sum the results of short-range correlations and of density fluctuation amplitudes which describe long-range correlations. In this paper we study the problem of relating the pseudopotentials to a (possibly singular) microscopic interaction with the aid of tools developed within the framework of the coupled cluster theory of K\"ummel and his collaborators, the results containing both familiar and unfamiliar elements. For example, the formulas derived, which depend on Bethe-Goldstone and Bethe-Faddeev amplitudes, include new definitions of particle-hole scattering matrix elements. An important consistency check is satisfied, in that the problem of defining the phenomenological potentials in terms of the microscopic ones must yield two separate but equivalent solutions, once within the framework of the theory of the ground-state energy and a second time within the framework of the theory of excitations. The entire package is studied with the aid of a modified version of coupled cluster theory, and shown to form a self-consistent entity. Among the desirable features of the formalism is that the large gap in the single-particle energy spectrum often utilized in existing formalisms is naturally absent from the current one.

Richard R. Chasman, John W. Durso