Spurious states in boson mapping

Kosuke Takada

P. Navrátil, H. B. Geyer, Jan Dobeš +1 more

Osvaldo Civitarese, H. B. Geyer, M. Reboiro

Implementation of Dyson boson mapping is discussed in connection with effective Hamiltonians. A feature of the mapping technique, when implemented in an ideal boson basis, is the possible appearance of spurious states. These spurious states typically signal the overcompleteness of the basis. Without truncation, no contamination of the physical states and spectrum takes place. However, in practice one may be required to select from the ideal boson basis the dominant components for a given interaction. It is shown that the correspondence between a perturbative expansion, $\'a\mathit{la}$ Bloch-Horowitz, and Dyson boson mapping allows for the identification of spurious states. The proposed method is applied to the mapping of a bi-fermionic Hamiltonian.

F.J.W. Hahne, H. B. Geyer, C. A. Engelbrecht

By stressing the application of boson mapping techniques to the truncated collective branch of nuclear excitations, the usefulness of two recently developed methods for the treatment of spurious states are compared. It is shown why the identification proposed by Geyer et al. is superior to the use of the ``Majorana'' operator S as proposed by Park.

J. DOBACZEWSKl, Jan Dobeš, H. B. Geyer +3 more

G.-K. Kim, C. Martin Vincent

The spurious state problem is generalized Dyson boson mapping is examined. For cases where the fermion space is restricted to at most four-quasiparticle excitations, we show that Dyson boson images of normal-ordered quasiparticle interactions have identically vanishing matrix elements in the unphysical boson space. This ``decoupling'' feature explains the finding of previous authors that, in systems with at most four quasiparticles, every spurious state appears at its unperturbed energy. However, we show that the decoupling property does not generally hold in problems where there are excitations of more than four quasiparticles. Claims about methods for the spurious state problem, even though verified in four-quasiparticle calculations, may therefore be of limited validity.