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

Journal of Experimental and Theoretical Physics Letters

Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum

Vladimir Georgievich Marikhin

Published Jul 1, 1996• 0 citations
Publisher

Abstract

The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ 0 and $$\hat H_0 $$ , where $$\hat H_0 + \hat V$$ 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.

DOI
10.1134/1.567160

Related papers

Orthogonality exponent and the friction coefficient of an electron gas

Kurt Schönhammer

The Anderson orthogonality exponent K for the overlap of two ground states of a free-electron gas with a local potential at different positions is discussed. In the small-distance limit, it is shown that for arbitrary local potentials K can be expressed in terms of the friction tensor. In the one-dimensional case, K depends on the potential only via the friction coefficient for arbitrary distance, and the exponent is bounded for arbitrary shape of the potential in contrast to the two- or higher-dimensional case. The exact result for K is presented for a short-range potential on a lattice.

Physical review. B, Condensed matter•May 1, 1991•11 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

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 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

Anderson’s orthogonality catastrophe in one dimension induced by a magnetic field

Hans Konrad Knörr, Peter Otte, Wolfgang Spitzer

According to Anderson's orthogonality catastrophe, the overlap of the N -particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various boundary conditions are employed. Unlike the usual setup the perturbation is introduced by a magnetic (vector) potential. Although such a magnetic field can be gauged away in one spatial dimension there is a significant and interesting effect on the overlap caused by the phases. We study the leading asymptotics of the overlap of the two ground states and the two-term asymptotics of the difference of the ground-state energies. In the case of periodic boundary conditions our main result on the overlap is based upon a well-known asymptotic expansion by Fisher and Hartwig on Toeplitz determinants with a discontinuous symbol. In the case of Dirichlet boundary conditions no such result is known to us and we only provide an upper bound on the overlap, presumably of the right asymptotic order.

arXiv:1502.07507•Journal of Physics A Mathematical and Theoretical•Jul 24, 2015•7 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
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.
The Anderson orthogonality exponent K for the overlap of two ground states of a free-electron gas with a local potential at different positions is discussed. In the small-distance limit, it is shown that for arbitrary local potentials K can be expressed in terms of the friction tensor. In the one-dimensional case, K depends on the potential only via the friction coefficient for arbitrary distance, and the exponent is bounded for arbitrary shape of the potential in contrast to the two- or higher-dimensional case. The exact result for K is presented for a short-range potential on a lattice.
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.
According to Anderson's orthogonality catastrophe, the overlap of the N -particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various boundary conditions are employed. Unlike the usual setup the perturbation is introduced by a magnetic (vector) potential. Although such a magnetic field can be gauged away in one spatial dimension there is a significant and interesting effect on the overlap caused by the phases. We study the leading asymptotics of the overlap of the two ground states and the two-term asymptotics of the difference of the ground-state energies. In the case of periodic boundary conditions our main result on the overlap is based upon a well-known asymptotic expansion by Fisher and Hartwig on Toeplitz determinants with a discontinuous symbol. In the case of Dirichlet boundary conditions no such result is known to us and we only provide an upper bound on the overlap, presumably of the right asymptotic order.