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

physica status solidi (b)

Decoupling approach for the Hubbard model

Lew Gehlhoff

Published Feb 1, 1996• 0 citations
Publisher

Abstract

Abstract The U = ∞ one‐band Hubbard model with large spin degeneracy N formulated with X operators is considered. The single‐particle Green's function is determined by applying the equation‐of‐motion method and a decoupling approach which is exact in the large‐N limit.
DOI
10.1002/pssb.2221930216

Related papers

MODIFIED HUBBARD DECOUPLING FOR THE EMERY MODEL

Lew Gehlhoff

We consider a version of the Emery model with large spin degeneracy N and use the X-operator formulation and the equation-of-motion method to determine the single-particle Green’s functions. We propose a modified Hubbard decoupling technique for the higher-order Green’s functions appearing in this equation of motion. By applying it to the above model in the limit N→∞ we obtain the exact results.

Modern Physics Letters B•Oct 30, 1995•0 citations

1/N expansions for the U = ∞ Hubbard model: Comparison between X‐operator and slave‐boson approach

Lew Gehlhoff

Abstract We consider the large‐spin‐degeneracy (N) version of the U = ∞ one‐band Hubbard model and present a systematic 1/N expansion method which is based on Hubbard's X‐operator formulation and a Baym‐Kadanoff expansion. We compare this alternative X‐operator approach with the customary time‐continuum slave‐boson (SB) functional‐integral treatment, which has recently been criticized. In particular, we give a detailed derivation of the density Green's function within the new approach and compare the leading‐order results with those as obtained with the commonly used SB treatment, finding total agreement.

physica status solidi (b)•Oct 1, 1996•1 citation

New approach to strongly correlated systems: 1N expansions without slave bosons

Andrei E. Ruckenstein, Stefan Schmitt-Rink

We introduce a new approach to strongly correlated systems, based on equations of motion for composite ("quasiparticle") operators. Conserving approximations to the appropriate Green's functions are generated through functional differentiation. For illustration, we apply this scheme to the infinite-$U$, single-band Hubbard model. The analogue of the Hartree-Fock approximation becomes exact in the limit of infinite spin degeneracy ($N$), while the random-phase approximation leads to the corresponding $\frac{1}{N}$ fluctuations.

Physical review. B, Condensed matter•Oct 1, 1988•62 citations

Equation-of-motion approach to the Hubbard model in infinite dimensions

Claudius Gros

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, ${\mathit{G}}^{(\mathit{n})}$(\ensuremath{\omega}), n=2,3,.... The first n-1 equations of motion are exactly fullfilled by ${\mathit{G}}^{(\mathit{n})}$(\ensuremath{\omega}) and the nth equation of motion is decoupled following a simple set of decoupling rules. ${\mathit{G}}^{(2)}$(\ensuremath{\omega}) corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for n=2,3,4.

arXiv:cond-mat/9403030•Physical review. B, Condensed matter•Sep 15, 1994•29 citations

Extended Hubbard model in the presence of a magnetic field

Francesco Paolo Mancini, Francesco Paolo Mancini

Abstract. Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature

•Nov 20, 2012•8 citations

An asymptotically exact mean-field approach for Hubbard X-operators

Alex C. Hewson, Allen L. Wasserman

The authors consider a systematic projection method for terminating the Green function equations of motion for Hubbard X-operators. This gives a set of mean fields that depend on the operators chosen. When applied to lowest order in the N-fold-degenerate U to infinity Anderson model an expression for the one-electron Green function is obtained that is exact for N=1 and in the limit N to infinity . This approach avoids the necessity of introducing auxiliary fields, such as constraint fields or slave bosons, to obtain asymptotically exact mean fields in the large-N limit and has general applicability in similar strongly correlated problems.

Journal of Physics Condensed Matter•Jan 16, 1989•3 citations
Abstract We consider the large‐spin‐degeneracy (N) version of the U = ∞ one‐band Hubbard model and present a systematic 1/N expansion method which is based on Hubbard's X‐operator formulation and a Baym‐Kadanoff expansion. We compare this alternative X‐operator approach with the customary time‐continuum slave‐boson (SB) functional‐integral treatment, which has recently been criticized. In particular, we give a detailed derivation of the density Green's function within the new approach and compare the leading‐order results with those as obtained with the commonly used SB treatment, finding total agreement.
We introduce a new approach to strongly correlated systems, based on equations of motion for composite ("quasiparticle") operators. Conserving approximations to the appropriate Green's functions are generated through functional differentiation. For illustration, we apply this scheme to the infinite-UUU, single-band Hubbard model. The analogue of the Hartree-Fock approximation becomes exact in the limit of infinite spin degeneracy (NNN), while the random-phase approximation leads to the corresponding 1N\frac{1}{N}N1​ fluctuations.
We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, G(n){\mathit{G}}^{(\mathit{n})}G(n)(\ensuremath{\omega}), n=2,3,.... The first n-1 equations of motion are exactly fullfilled by G(n){\mathit{G}}^{(\mathit{n})}G(n)(\ensuremath{\omega}) and the nth equation of motion is decoupled following a simple set of decoupling rules. G(2){\mathit{G}}^{(2)}G(2)(\ensuremath{\omega}) corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for n=2,3,4.
The authors consider a systematic projection method for terminating the Green function equations of motion for Hubbard X-operators. This gives a set of mean fields that depend on the operators chosen. When applied to lowest order in the N-fold-degenerate U to infinity Anderson model an expression for the one-electron Green function is obtained that is exact for N=1 and in the limit N to infinity . This approach avoids the necessity of introducing auxiliary fields, such as constraint fields or slave bosons, to obtain asymptotically exact mean fields in the large-N limit and has general applicability in similar strongly correlated problems.