Dyson boson mapping of effective bi-fermion Hamiltonians

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, $á\mathit{la}$ 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.

Figure 1

Eigenvalues $E_{n=1}$ and $E_{n=2}$, solid lines, and expectation values of $h^{(2)}$, dotted lines. The values are display as a functions of the strength V, for different values of $L=\lambda +\mu$. Cases (a), (b), and (c) correspond to $L=0,\hspace{1em}1,\hspace{1em}$ and 2 MeV, respectively. All results correspond to $\Omega =5$, the value of $E_0$ of Eq. (26) is fixed at $E_0=1$, and all values are given in units of mega-electron volts.

Figure 2

Same as Fig. 1 for $\Omega =10$.