The interacting boson approximation model and applications

Abraham Klein, Jin Quan Chen

We derive an approximate boson-quasifermion mapping of a single-j shell-model algebra, applicable to the seniority classification scheme, as an expansion in the ratio of the seniority quantum number to the level degeneracy, with selective summation of higher order terms. The procedure used is an extension of the algebraic technique first applied to the purely bosonic part of the mapping by Bonatsos, Klein, and Li. Only the maps of the generators are needed to derive a Hamiltonian for the interacting boson fermion model (IBFM), and these can be obtained in Hermitian form without having to go through the intermediary of a mapping of the fermion operators. Application of the results is illustrated by a fresh discussion of the so-called exchange interaction of the IBFM. A consistent mapping of the single fermion in terms of bosons and quasifermions is also derived that includes a consideration of the unusual properties of the quasifermions.

Simon Peter Rosen

Erik G. C. P. van Loon, Malte Schüler, Mikhail I. Katsnelson +1 more

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant quantum Monte Carlo simulations of the effective Hubbard model.

Abraham Klein

昂亮 野村

С.П. Иванова, R. V. Jolos, R. Pedrosa

The generalised Holstein-Primakoff boson representation of the bifermion operators is used to construct a boson image of the microscopic nuclear Hamiltonian. The microscopic analogue of the interacting boson model (IBM) Hamiltonian is obtained. It is shown how the square-root factor in the IBM Hamiltonian can be generalised so as to take into account its dependence on the angular momentum and seniority of the collective state. The method is applicable to systems where the assumption that the projection operator P is approximately equal to unity can be used. The method is proposed to include, apart from the collective quadrupole, other collective and non-collective degrees of freedom in the Hamiltonian.