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Title: Two-impurity Anderson model: A variational study

Abstract

A comprehensive variational study of the two-impurity Anderson model is presented. First a lowest-order basis is introduced, which does not contain electronic excitations above the Fermi level: in this basis, the indirect [ital f]-[ital f] interaction of the form [minus][ital J][bold S][sub 1][center dot][bold S][sub 2] is not generated but is added by hand. The effect of electron-hole (EH) excitations is also studied. A suitable discretization of the continuous band spectrum allows us to obtain all eigenvalues and eigenvectors and to calculate finite-temperature magnetic properties. For a distance [ital R][gt][ital R][sub [ital c]], where [ital R][sub [ital c]][similar to]2.5([ital k][sub [ital F]])[sup [minus]1] ([ital k][sub [ital F]] is the Fermi wave vector), the interference between screening clouds around the two impurities is weak and the physics depends smoothly on the ratio between the coupling [ital J] and the Kondo temperature [ital T][sub [ital K]]. In this regime, the effect of EH excitations is to renormalize the [ital f]-level energy and to add the magnetic interaction. At finite temperature, the results of scaling theory and of quantum Monte Carlo simulations are recovered, with growth of magnetic correlations down to temperatures [ital T][similar to][ital T][sub [ital K]] and a two-stage Kondo effectmore » for [ital J][much gt][ital T][sub [ital K]]. For [ital R][r arrow]0, the impurity spins lock in a triplet and the binding energy is exponentially increased, indicating that a collective Kondo effect takes place. At zero distance, only a half of the total impurity moment is compensated at low temperature. The magnetic interaction now competes with the enhanced binding energy. It is argued that the short-distance beahvior of the two-impurity model is not representative of the properties of the periodic Anderson model close to half-filling.« less

Authors:
 [1];  [2]
  1. Institut Romand de Recherche Numerique en Physique des Materiaux (IRRMA), PHB-Ecublens, CH-1015 Lausanne (Switzerland) Dipartimento di Fisica A. Volta,'' Universita di Pavia, via Bassi 6, I-27100 Pavia (Italy)
  2. Institut de Physique, Universite de Neuchatel, rue A.-L. Breguet 1, CH-2000 Neuchatel (Switzerland)
Publication Date:
OSTI Identifier:
6242043
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter; (United States)
Additional Journal Information:
Journal Volume: 48:10; Journal ID: ISSN 0163-1829
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; IMPURITIES; MAGNETIC PROPERTIES; ELECTRONIC STRUCTURE; F STATES; KONDO EFFECT; TEMPERATURE DEPENDENCE; VARIATIONAL METHODS; CALCULATION METHODS; ENERGY LEVELS; PHYSICAL PROPERTIES; 665400* - Quantum Physics Aspects of Condensed Matter- (1992-)

Citation Formats

Andreani, L C, and Beck, H. Two-impurity Anderson model: A variational study. United States: N. p., 1993. Web. doi:10.1103/PhysRevB.48.7322.
Andreani, L C, & Beck, H. Two-impurity Anderson model: A variational study. United States. https://doi.org/10.1103/PhysRevB.48.7322
Andreani, L C, and Beck, H. Wed . "Two-impurity Anderson model: A variational study". United States. https://doi.org/10.1103/PhysRevB.48.7322.
@article{osti_6242043,
title = {Two-impurity Anderson model: A variational study},
author = {Andreani, L C and Beck, H},
abstractNote = {A comprehensive variational study of the two-impurity Anderson model is presented. First a lowest-order basis is introduced, which does not contain electronic excitations above the Fermi level: in this basis, the indirect [ital f]-[ital f] interaction of the form [minus][ital J][bold S][sub 1][center dot][bold S][sub 2] is not generated but is added by hand. The effect of electron-hole (EH) excitations is also studied. A suitable discretization of the continuous band spectrum allows us to obtain all eigenvalues and eigenvectors and to calculate finite-temperature magnetic properties. For a distance [ital R][gt][ital R][sub [ital c]], where [ital R][sub [ital c]][similar to]2.5([ital k][sub [ital F]])[sup [minus]1] ([ital k][sub [ital F]] is the Fermi wave vector), the interference between screening clouds around the two impurities is weak and the physics depends smoothly on the ratio between the coupling [ital J] and the Kondo temperature [ital T][sub [ital K]]. In this regime, the effect of EH excitations is to renormalize the [ital f]-level energy and to add the magnetic interaction. At finite temperature, the results of scaling theory and of quantum Monte Carlo simulations are recovered, with growth of magnetic correlations down to temperatures [ital T][similar to][ital T][sub [ital K]] and a two-stage Kondo effect for [ital J][much gt][ital T][sub [ital K]]. For [ital R][r arrow]0, the impurity spins lock in a triplet and the binding energy is exponentially increased, indicating that a collective Kondo effect takes place. At zero distance, only a half of the total impurity moment is compensated at low temperature. The magnetic interaction now competes with the enhanced binding energy. It is argued that the short-distance beahvior of the two-impurity model is not representative of the properties of the periodic Anderson model close to half-filling.},
doi = {10.1103/PhysRevB.48.7322},
url = {https://www.osti.gov/biblio/6242043}, journal = {Physical Review, B: Condensed Matter; (United States)},
issn = {0163-1829},
number = ,
volume = 48:10,
place = {United States},
year = {1993},
month = {9}
}