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Communications in Theoretical Physics

Abelian Bosonization Approach, to a Magnetic Impurity Model

Zhang GuangMing

Published Sep 15, 2000• 4 citations
Publisher

Abstract

Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.

DOI
10.1088/0253-6102/34/2/211

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Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.
The low-temperature properties of the SU(N)(N)(N) Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low-temperature properties of the model. The single-particle Green's function is enhanced due to the presence of local correlation. The basic correlation functions such as the charge or spin correlator are also influenced by the presence of impurity, and show local Fermi liquid behavior. The x-ray absorption is affected by the presence of the local Hubbard interaction. The exponent is decreased (increased) for repulsive (attractive) interactions.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension D=1,2,D=1,2,D=1,2, and 3.3.3. For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.$ In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T1.{1/T}_{1}.1/T1​.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e. the Hubbard model in the spatial dimension D=1,2,D=1,2,D=1,2, and 3. For the 1D system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, 1/T1T∼χ21/T_1T \sim \chi^21/T1​T∼χ2. In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T11/T_11/T1​.
We show that the functional renormalization group is a numerically cheap method to obtain the low-energy behavior of the Anderson impurity model describing a localized impurity level coupled to a bath of conduction electrons. Our approach uses an external magnetic field as the flow parameter, partial bosonization of the transverse spin fluctuations, and frequency-independent interaction vertices determined by Ward identities. The magnetic field serves also as a regulator for the bosonized spin fluctuations, which are suppressed at large field. We calculate the quasiparticle residue and spin susceptibility in the particle-hole symmetric case and obtain excellent agreement with the Bethe ansatz results for arbitrary coupling.