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

Journal of Low Temperature Physics

Consistent 1/N-expansion for the four-slave-boson approach with an appropriate operator-ordering prescription

Enrico Aarrigoni, Giancarlo Calvanese Strinati

Published May 1, 1995• 1 citation
Publisher
DOI
10.1007/bf00752348

Related papers

Revising the 1/N Expansion for the Slave-Boson Approach within the Functional Integral

Enrico Arrigoni, Claudio Castellani, Roberto Raimondi +1 more

NATO ASI series. Series B : Physics•Jan 1, 1995•0 citations

Exact criterion for choosing the hopping operator in the four-slave-boson approach

Enrico Arrigoni, Giancarlo Calvanese Strinati

We consider the N-component generalization of the four-slave-boson approach to the Hubbard model, where 1/N acts as the small parameter that controls the fluctuations about the saddle point, and address the problem of the appropriate choice of the bosonic hopping operator ${\mathit{z}}_{\mathit{i}\mathrm{\ensuremath{\sigma}}}$. By suitably reorganizing the Fock space, we show that the square-root form for ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$ (originally introduced by Kotliar and Ruckenstein) reproduces the exact independent-fermion (U=0) results not only at the mean-field (N=\ensuremath{\infty}) level but also to all orders in the 1/N expansion, provided one relaxes the usually adopted normal-ordered prescription for ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$. This ensures that ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$ need not be modified at successive orders in the fluctuation expansion, and implies that all correlation functions are correctly recovered in the U=0 limit, a nontrivial result for the slave-boson approach. In addition, it provides a stringent requirement on the form of ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$, which might be also generalized to alternative slave-boson formalisms (like the spin-rotation-invariant formulation).

arXiv:cond-mat/9508058•Physical review. B, Condensed matter•Nov 15, 1995•3 citations

Dobiński relations and ordering of boson operators

Paweł Błasiak, Agnieszka Gawron, A. Horzela +2 more

Czechoslovak Journal of Physics•Oct 1, 2006•2 citations

Correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase

Enrico Arrigoni, Giancarlo Calvanese Strinati

The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean field are considered, thus removing the inconsistencies originating from the incorrect handling of this pathologic limit so far performed in the literature. In particular, our treatment correctly restores the decrease of the average number of doubly occupied sites for increasing U. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.

arXiv:cond-mat/9501132•Physical review. B, Condensed matter•Jul 15, 1995•14 citations

Exact boson expansion for spin- systems

H. Barentzen

Physics Letters A•Jul 1, 1991•3 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
We consider the N-component generalization of the four-slave-boson approach to the Hubbard model, where 1/N acts as the small parameter that controls the fluctuations about the saddle point, and address the problem of the appropriate choice of the bosonic hopping operator ${\mathit{z}}_{\mathit{i}\mathrm{\ensuremath{\sigma}}}$. By suitably reorganizing the Fock space, we show that the square-root form for ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$ (originally introduced by Kotliar and Ruckenstein) reproduces the exact independent-fermion (U=0) results not only at the mean-field (N=\ensuremath{\infty}) level but also to all orders in the 1/N expansion, provided one relaxes the usually adopted normal-ordered prescription for ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$. This ensures that ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$ need not be modified at successive orders in the fluctuation expansion, and implies that all correlation functions are correctly recovered in the U=0 limit, a nontrivial result for the slave-boson approach. In addition, it provides a stringent requirement on the form of ${\mathit{z}}_{\mathit{i},\mathrm{\ensuremath{\sigma}}}$, which might be also generalized to alternative slave-boson formalisms (like the spin-rotation-invariant formulation).
The Hubbard model with finite on-site repulsion U is studied via the functional-integral formulation of the four-slave-boson approach by Kotliar and Ruckenstein. It is shown that a correct treatment of the continuum imaginary time limit (which is required by the very definition of the functional integral) modifies the free energy when fluctuation (1/N) corrections beyond mean field are considered, thus removing the inconsistencies originating from the incorrect handling of this pathologic limit so far performed in the literature. In particular, our treatment correctly restores the decrease of the average number of doubly occupied sites for increasing U. Our analysis requires us to suitably interpret the Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon the commonly used normal-ordering prescription, in order to obtain meaningful fluctuation corrections. In this way we recover the exact solution at U=0 not only at the mean-field level but also at the next order in 1/N. In addition, we consider alternative choices for the bosonic hopping operator and test them numerically for a simple two-site model for which the exact solution is readily available for any U. We also discuss how the 1/N expansion can be formally generalized to the four-slave-boson approach, and provide a simplified prescription to obtain the additional terms in the free energy which result at the order 1/N from the correct continuum limit.
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.