Pairing ground states in fermion systems: A static method

Abstract

We present a static recursive method that can straightforwardly be applied to variational treatments of canonical many-body systems whose ground states generally exhibit pairing or higher clustering correlations. We illustrate the utility of the method by applying it to an electron system with pairing interactions where we obtain, as expected, a smooth transition between a Bose condensate of tightly bound electron pairs and a superconducting ground state. The method also reproduces the mean-field results for the electron-hole liquid problem as well as the antiferromagnetic insulator ground state of the Hubbard model but in a simpler way. We give a nontrivial application to a model of dense molecular hydrogen consisting of condensed generalized molecules. We show that the effective interaction between identical particles is of such a form that the state undergoes a dielectric catastrophe at a certain finite density. The competition between this abrupt transition and a smooth transition of atomic pairs in the spinless and translationally invariant version of the problem is also discussed.