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Annals of Physics

Theory of quasimagnetic impurity in a metal: An exactly soluble model of interacting electrons

Daniel Charles Mattis

Published Jan 1, 1975• 13 citations
Publisher
DOI
10.1016/0003-4916(75)90295-x

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Band theory of magnetism in metals in context of exactly soluble model

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The role of spatial forces, and of Hund's rule (exchange) forces, and the validity of the Hartree-Fock approximation in the band theory of magnetism of metals is reviewed. Some reasonable conjectures which have been made elsewhere by the author and others are examined in the light of an exactly soluble model of interacting electrons in one dimension. It is shown that within the framework of validity of this model, spatial i.e., direct (Coulomb) forces do not influence the spin susceptibility, and conversely, Hund's rule exchange forces do not affect the dielectric constant or plasmon spectrum. It is recalled that the time-independent Hartree-Fock approximation yields an incorrect spectrum of elementary excitations, and it is also shown explicitly that the magnetic susceptibility calculated in this approximation is incorrect. A paradox is noted, concerning whether ``correlations'' can in fact correct the errors in the H-F approximation. Finally, it is shown that when there are only space forces, such spin density waves as might be introduced in to the H-F ground state of the model are in fact spurious, because they are not representative of the correlations which exist in the true ground state.

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Materials classified as strongly-correlated systems often exhibit complex and fascinating properties due to interactions among electrons as well as between electrons and other constituents of the material. A common model to describe electronic system with strong on-site Coulomb interaction is Hubbard model. One very powerful approximation method for solving Hubbard model having been widely used over the last few decades is dynamical mean-field theory (DMFT). This method maps the original lattice problem into an impurity problem embedded in a self-consistent bath. Apart from the many variants of implementation of DMFT, it relies on using an impurity solver as part of its algorithm. In this work, rather than solving a Hubbard model, we propose to explore the impurity solver itself for solving a problem of metallic host doped with correlated elements, commonly referred to as Anderson impurity model (AIM). We solve the model using the distributional exact diagonalisation method. Our particular aim is to show how the metal-insulator transition (MIT) occurs in the system and how the phenomenon reflects in its optical conductivity for various model parameters.

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Using notions of supersymmetry, we present an exactly soluble model of anyons with both statistical and scalar interactions in 2+1 dimensions. We demonstrate that half-statistics particles with two spin flavors condense into a local singlet state which is both a charge superfluid and a ``spin metal'' in the sense that there is charge-pairing off-diagonal long-range order with gapless charge excitations, but a gap in the collective spin-mode spectrum. The present results shed considerable light on the mean-field theory of fractional statistics.

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Theory of diamagnetic susceptibility of interacting electrons in solids

S.P. Mohanty, P. K. Misra

Physics Letters A•Jun 1, 1974•3 citations
The role of spatial forces, and of Hund's rule (exchange) forces, and the validity of the Hartree-Fock approximation in the band theory of magnetism of metals is reviewed. Some reasonable conjectures which have been made elsewhere by the author and others are examined in the light of an exactly soluble model of interacting electrons in one dimension. It is shown that within the framework of validity of this model, spatial i.e., direct (Coulomb) forces do not influence the spin susceptibility, and conversely, Hund's rule exchange forces do not affect the dielectric constant or plasmon spectrum. It is recalled that the time-independent Hartree-Fock approximation yields an incorrect spectrum of elementary excitations, and it is also shown explicitly that the magnetic susceptibility calculated in this approximation is incorrect. A paradox is noted, concerning whether ``correlations'' can in fact correct the errors in the H-F approximation. Finally, it is shown that when there are only space forces, such spin density waves as might be introduced in to the H-F ground state of the model are in fact spurious, because they are not representative of the correlations which exist in the true ground state.
Materials classified as strongly-correlated systems often exhibit complex and fascinating properties due to interactions among electrons as well as between electrons and other constituents of the material. A common model to describe electronic system with strong on-site Coulomb interaction is Hubbard model. One very powerful approximation method for solving Hubbard model having been widely used over the last few decades is dynamical mean-field theory (DMFT). This method maps the original lattice problem into an impurity problem embedded in a self-consistent bath. Apart from the many variants of implementation of DMFT, it relies on using an impurity solver as part of its algorithm. In this work, rather than solving a Hubbard model, we propose to explore the impurity solver itself for solving a problem of metallic host doped with correlated elements, commonly referred to as Anderson impurity model (AIM). We solve the model using the distributional exact diagonalisation method. Our particular aim is to show how the metal-insulator transition (MIT) occurs in the system and how the phenomenon reflects in its optical conductivity for various model parameters.
Using notions of supersymmetry, we present an exactly soluble model of anyons with both statistical and scalar interactions in 2+1 dimensions. We demonstrate that half-statistics particles with two spin flavors condense into a local singlet state which is both a charge superfluid and a ``spin metal'' in the sense that there is charge-pairing off-diagonal long-range order with gapless charge excitations, but a gap in the collective spin-mode spectrum. The present results shed considerable light on the mean-field theory of fractional statistics.