arXiv:cond-mat/9305028 · Physical review. B, Condensed matter

Asymptotically exact mean-field theory for the Anderson model including double occupancy

J. Holm, Reiner Kree, Kurt Schönhammer

Published Aug 15, 1993• 13 citations

Abstract

The Anderson impurity model for finite values of the Coulomb repulsion U is studied using a slave-boson representation for the empty and doubly occupied f level. In order to avoid well-known problems with a naive mean-field theory for the boson fields, we use the coherent-state-path integral representation to first integrate out the double-occupancy slave bosons. The resulting effective action is linearized using two-time auxiliary fields. After integration over the fermionic degrees of freedom, one obtains an effective action suitable for a 1/${\mathit{N}}_{\mathit{f}}$ expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and ${\mathit{N}}_{\mathit{f}}$\ensuremath{\rightarrow}\ensuremath{\infty}, exact results for the ground-state properties are recovered in the saddle-point approximation. Numerical solutions of the saddle-point equations show that even in the spin-degenerate case ${\mathit{N}}_{\mathit{f}}$=2 the results are quite good.

DOI: 10.1103/physrevb.48.5077

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arXiv:cond-mat/9305028 · Physical review. B, Condensed matter

Asymptotically exact mean-field theory for the Anderson model including double occupancy

J. Holm, Reiner Kree, Kurt Schönhammer

Published Aug 15, 1993• 13 citations

arXiv HTML PDF

Abstract

{\mathit{N}}_{\mathit{f}}

expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and

{\mathit{N}}_{\mathit{f}}

\ensuremath{\rightarrow}\ensuremath{\infty}, exact results for the ground-state properties are recovered in the saddle-point approximation. Numerical solutions of the saddle-point equations show that even in the spin-degenerate case

{\mathit{N}}_{\mathit{f}}

=2 the results are quite good.

DOI: 10.1103/physrevb.48.5077

Related papers

Importance of the local constraint in slave-boson theories

L. Zhang, Jainendra K. Jain, Victor J. Emery

Slave bosons are commonly introduced in order to implement an infinite Hubbard U by means of a local constraint. The usual starting point for investigations within this scheme is a mean-field theory in which the constraint is taken to be global. This approximate treatment of the constraint is studied in the context of a two-band Hubbard model, and it is shown that (i) the ground state has a significant number of doubly occupied sites, despite the infinite on-site repulsion in the original model, and (ii) there is an unphysical tendency for pairing. However, it is found that if the local constraint is retained for the insulator at half filling, then mean-field theory gives the correct result that the double occupancy is zero.Slave bosons are commonly introduced in order to implement an infinite Hubbard U by means of a local constraint. The usual starting point for investigations within this scheme is a mean-field theory in which the constraint is taken to be global. This approximate treatment of the constraint is studied in the context of a two-band Hubbard model, and it is shown that (i) the ground state has a significant number of doubly occupied sites, despite the infinite on-site repulsion in the original model, and (ii) there is an unphysical tendency for pairing. However, it is found that if the local constraint is retained for the insulator at half filling, then mean-field theory gives the correct result that the double occupancy is zero.

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{\mathit{N}}_{\mathit{f}}

expansion. The same problem remains concerning the constraint as in the infinite U case. For T\ensuremath{\rightarrow}0 and

{\mathit{N}}_{\mathit{f}}

{\mathit{N}}_{\mathit{f}}

=2 the results are quite good.

U

single-impurity Anderson model with a nearest-neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion, which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation, we introduce appropriate weight factors in the KR saddle point scheme. Ground-state and all excitation levels agree with the exact diagonalization results. Thermodynamics and correlation functions may be recovered in a suitably renormalized saddle point evaluation.

{\mathit{N}}^{2}

) in the 1/N expansion of the functional-integral formalism. The obtained effective exchange coupling constant

{\mathit{J}}_{\mathrm{eff}}

(\ensuremath{\delta})=J(2

{\mathit{p}}_{0}^{2}

-\ensuremath{\delta}/2) with J\ensuremath{\equiv}

{\mathit{t}}_{\mathit{i}\mathit{j}}^{2}

/U is strongly dependent upon doping \ensuremath{\delta} and is scaled with the reduced Coulomb repulsion u\ensuremath{\equiv}U/

{\mathit{U}}_{\mathit{c}}

in the two-dimensional (2D) and 3D Hubbard models, where

{\mathit{U}}_{\mathit{c}}

is the critical value for the metal-to-insulator transition. The roles of this intersite correlation and the spin-dependent band-renormalization correlation included in the mean-field theory for the paramagnetic-to-antiferromagnetic instability are compared in the two Hubbard models. The intersite contribution is more significant in the 2D case than in the 3D case, but is generally small compared with the band effect except for small dopings \ensuremath{\delta} and smaller U values. The maximum doping ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$ for the paramagnetic-to-ferromagnetic instability in the strong-coupling limit (U\ensuremath{\rightarrow}\ensuremath{\infty}) of the 2D and 3D Hubbard models is found to be ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.28 and ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.38, respectively.

U

extensions of the noncrossing approximation, the method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low frequency. We demonstrate that this impurity solver can be applied in the context of dynamical mean-field theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.