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Progress of Theoretical Physics

Orthogonality Catastrophe for a System of Interacting Electrons. II

K. Yamada, Kei Yosida

Published Aug 1, 1979• 19 citations
Publisher

Abstract

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 operaors with off-diagonal elements. This orthogonality theorem expressed in a general form is applied to some special cases.

DOI
10.1143/ptp.62.363

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Journal of Experimental and Theoretical Physics Letters•Jul 1, 1996•0 citations
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 operaors with off-diagonal elements. This orthogonality theorem expressed in a general form is applied to some special cases.
We propose a simple calculation method for an overlap integral between two ground states of the system with a local potential at each different site. Our formalism is applied to the overlap integral limited to l-wave scattering and the exact result is obtained. We also apply our formalism to the overlap integral for the system with l- and l’-partial wave components of scattering. The overlap integral in this case is exactly obtained in a closed form as a function of the phase shifts of l- and l’-waves. Our result covers that of Yamada, Sakurai, Miyazima and Hwang.
The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ 0 and H^0\hat H_0 H^0​ , where H^0+V^\hat H_0 + \hat VH^0​+V^ is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M −1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained.