Abstract It is shown that a perturbation expansion for projected states proposed earlier satisfies the Schrödinger equation. Modified forms of the series are suggested, and criteria for their convergence are discussed. The method is applied to the ‘Lipkin model' for a two-level many-body problem, which is exactly soluble. The second-order term in the perturbation series is shown to give a good approximation, and is compared with alternative methods. The convergence factor of the series is shown to be better than that of ordinary perturbation theory, which in most cases of this model is divergent.Abstract It is shown that a perturbation expansion for projected states proposed earlier satisfies the Schrödinger equation. Modified forms of the series are suggested, and criteria for their convergence are discussed. The method is applied to the ‘Lipkin model' for a two-level many-body problem, which is exactly soluble. The second-order term in the perturbation series is shown to give a good approximation, and is compared with alternative methods. The convergence factor of the series is shown to be better than that of ordinary perturbation theory, which in most cases of this model is divergent.

Proceedings of the Royal Society of London A Mathematical and Physical SciencesNov 27, 197314 citations

Bound-state perturbation theory: A new approach

David Atkinson

Nuclear Physics BJun 1, 19704 citations

Mott transition near the ferromagnetic state

P. G. J. van Dongen, V. Janiš

We consider the Hubbard model, either in a magnetic field (model I) or with a general nearest-neighbor interaction (model II). For these models we determine criteria for the instability of the fully polarized ferromagnet. We show that the ground state below the instability contains an exactly soluble Mott transition. The transition occurs at a critical interaction ${\mathit{U}}_{\mathit{c}}$ , at which perturbation theory breaks down. Extended metallic states are found for U ${\mathit{U}}_{\mathit{c}}$ , insulating bound states for U> ${\mathit{U}}_{\mathit{c}}$ . Details of the transition strongly depend on dimension.We consider the Hubbard model, either in a magnetic field (model I) or with a general nearest-neighbor interaction (model II). For these models we determine criteria for the instability of the fully polarized ferromagnet. We show that the ground state below the instability contains an exactly soluble Mott transition. The transition occurs at a critical interaction ${\mathit{U}}_{\mathit{c}}$, at which perturbation theory breaks down. Extended metallic states are found for U${\mathit{U}}_{\mathit{c}}$, insulating bound states for U>${\mathit{U}}_{\mathit{c}}$. Details of the transition strongly depend on dimension.

Physical Review LettersMay 16, 199421 citations

{\mathit{U}}_{\mathit{c}}

, at which perturbation theory breaks down. Extended metallic states are found for U

{\mathit{U}}_{\mathit{c}}

, insulating bound states for U>

{\mathit{U}}_{\mathit{c}}

. Details of the transition strongly depend on dimension.