Orthogonality Catastrophe for a System of Interacting Electrons

It is shown that the overlap integral between two ground-state wave functions for the Hamiltonian of the interacting electron system with different local potentials can be written generally in terms of the S-matrix describing potential scattering. Here, the local potential is considered to be a general inseparable one and the Green functions and self-energies are treated as operators with off-diagonal elements. This orthogonality theorem expressed in a general form is applied to some special cases. In previous papers, 1''2l we have shown that the orthogonality theorem3 ' holds also in the system of interacting electrons. In those papers, we used the Anderson Hamiltonian. In this paper we consider the interacting electron system with a local potential which is general, and we show that the overlap integral can b