Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

New Formalism for an Overlap Integral of the Anderson Orthogonality Theorem

Akihide Oguchi, Kei Yosida

Published May 1, 1986• 7 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.75.1048

Related papers

Anderson Orthogonality Theorem: Overlap Integral between Two Ground States with Differnt Centers of Local Potential

T. Kitamura, Akihide Oguchi, Kei Yosida

The overlap integral between two ground states of the conduction electron system with a local potential at each different site is studied. The overlap integral is obtained for the system with 3 nonzero partial wave components of scattering, and this result is extended to the general case with n nonzero phase shifts. It is shown that the calculation of the exponent of the overlap integral can be reduced to solving an eigenvalue problem.

Progress of Theoretical Physics•Sep 1, 1987•3 citations

Overlap Integral between the Ground States of an Electron Gas Corresponding to Two Positions of a Scattering Potential

Károly Vladár

The exponent K in the Anderson orthogonality theorem is calculated for a heavy particle having two sites, when the electron scattering on one site involves n partial waves. K is given in closed expressions for n = 1 …4. Small and large translations of the scattering center and the weak scattering are discussed at arbitrary n. The partial wave l cannot contribute by more than l + (1/2) to K.

Progress of Theoretical Physics•Jul 1, 1993•4 citations

Orthogonality Catastrophe for a System of Interacting Electrons

Kei Yamada, Kei Yosida

The Anderson theorem concerning the overlap integral between two ground-state wave-functions of the electron system with different local potentials is discussed from a general point of view. It is shown that this theorem generally holds in the case where the initial Hamiltonian also includes electron interactions.

Progress of Theoretical Physics•Aug 1, 1978•14 citations

Orthogonality Catastrophe Due to Local Electron Interaction

K. Yamada, Kei Yosida

The overlap integral between two ground state wave functions of the conduction electron system with different local situations is discussed for a general case in which local electron interaction exists in addition to a local impurity potential. The Anderson theorem which states that the overlap integral is expressed by exp[-δ/π×logN] is proved in this general case.

Progress of Theoretical Physics•Apr 1, 1978•21 citations

Orthogonality Catastrophe for a System of Interacting Electrons. II

K. Yamada, Kei Yosida

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.

Progress of Theoretical Physics•Aug 1, 1979•19 citations

Exact Calculation of the Orthogonality Catastrophe in Metals

N. Rivier, Eugen Šimánek

We give exact calculation, using the linked-cluster theorem, of the overlap between the ground-state wave functions of a system of $N$ fermions in the absence and in the presence of a localized potential. It is found that the overlap vanishes as ${N}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}(\ensuremath{\delta})$ contains both a nonperiodic and a $\ensuremath{\pi}$-periodic term in the phase shift $\ensuremath{\delta}({\ensuremath{\epsilon}}_{\mathrm{F}})$ due to the potential. The present result reduces to that of Anderson and of Nozi\`eres and de Dominicis for small phase shifts.

Physical Review Letters•Feb 22, 1971•22 citations
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.
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 give exact calculation, using the linked-cluster theorem, of the overlap between the ground-state wave functions of a system of NNN fermions in the absence and in the presence of a localized potential. It is found that the overlap vanishes as ${N}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}(\ensuremath{\delta})$ contains both a nonperiodic and a $\ensuremath{\pi}$-periodic term in the phase shift $\ensuremath{\delta}({\ensuremath{\epsilon}}_{\mathrm{F}})$ due to the potential. The present result reduces to that of Anderson and of Nozi\`eres and de Dominicis for small phase shifts.