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

arXiv:cond-mat/9911255 · Physical review. B, Condensed matter

Strong-coupling approach for strongly correlated electron systems

Andrij M. Shvaika

Published Jul 15, 2000• 14 citations
arXivHTMLPDF

Abstract

A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each vertex the problem splits into the subspaces with ``vacuum states'' determined by the diagonal Hubbard operators and only excitations around these vacuum states are allowed. The rules to construct diagrams are proposed. In the limit of infinite spatial dimensions the total auxiliary single-site problem exactly splits into subspaces that allows to build an analytical thermodynamically consistent approach for a Hubbard model. Some analytical results are given for the simple approximations when the two-pole (alloy-analogy solution) and four-pole (Hartree-Fock approximation) structure for Green's function is obtained. Two poles describe contribution from the Fermi-liquid component, which is dominant for small electron and hole concentrations (``overdoped case'' of high-${T}_{c}'\mathrm{s}),$ whereas other two describe contribution from the non-Fermi liquid and are dominant close to half-filling (``underdoped case'').

DOI
10.1103/physrevb.62.2358

Related papers

STRONG COUPLING HARTREE-FOCK APPROXIMATION IN THE DYNAMICAL MEAN-FIELD THEORY

Andrij M. Shvaika

In the limit of infinite spatial dimensions, a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction ( U < ∞ ), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different "vacuum states".Some analytical results are given for the Hartree-Fock approximation when the 4pole structure for Green's function is obtained: two poles describe contribution from the Fermi liquid component, which is ferromagnetic and dominant for small electron and hole concentrations ("overdoped case" of high-T c 's), whereas other two describe contribution from the non-Fermi liquid, which is antiferromagnetic and dominant close to half filling ("underdoped case").

arXiv:cond-mat/0011407•Condensed Matter Physics•Jan 1, 2001•1 citation

Linked-cluster expansion around the atomic limit of the Hubbard model

Walter Metzner

We develop a perturbation expansion in the intersite hopping around the atomic limit of the Hubbard model. It is valid for arbitrary finite temperatures and interaction strengths. Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived. They reduce the calculation of any finite-order contribution to simple algebra. This opens the way for series extrapolations from computer-aided high-finite-order evaluations. Discrepancies in earlier expansions around the atomic limit are clarified. The present expansion scheme involves only connected diagrams with unrestricted lattice sums. This allows one to perform a vertex renormalization as for the linked-cluster expansion of the Ising model. The renormalized perturbation expansion can be used to construct self-consistent approximations which are automatically exact in the atomic limit. In the limit of high lattice dimensions, only fully two-particle reducible embeddings of diagrams on the lattice contribute. The single-particle properties of the infinite-dimensional Hubbard model reduce to those of independent tight-binding fermions hopping between dressed sites.

Physical review. B, Condensed matter•Apr 1, 1991•239 citations

APPROXIMATE ANALYTICAL DYNAMICAL MEAN-FIELD APPROACH TO STRONGLY CORRELATED ELECTRON SYSTEMS

Stasyuk

An approximate analytical scheme of the dynamical mean-field theory (DMFT), that is used for electron systems with Hubbard correlations and is exact in the limit of the infinite dimensionality of a space, is developed.The effective single-site problem arising in the framework of this method is formulated in terms of the auxiliary Fermi-field.The irreducible Green's function technique with the projecting on the Hubbard basis of Fermi-operators is used for its solution.A system of DMFT equations is obtained in the approximation which is a generalization of the Hubbard-III approximation and combines it with a self-consistent renormalization of the local electron levels.It is shown that the proposed approach includes as simple specific cases a number of known approximations (Hubbard-III, AA, MAA, . . . ) based on the assumption of the single-site structure of the electron selfenergy.

Condensed Matter Physics•Jan 1, 2000•9 citations

THE SINGLE-SITE APPROXIMATION TO THE HUBBARD MODEL

MASSIMO CORRIAS

The diagrammatic formulation of the single-site approximation to the Hubbard model immediately yields the exact solution to the Falikov-Kimball model in infinite dimensions. By an extension of the alloy analogy, we then derive a two-fluid model, dividing self-consistently the electron system among itinerating and relatively localized particles. Our theory coincides with the CPA only the at half-filling and u=∞. We start by studying the mean field approximation to our theory and identify a phase boundary in the particle density-interaction strength (n−u) plane at which the Fermi liquid model breaks down. Then the effect of fluctuations in the Fermi liquid regime is considered and, finally, we construct, at half-filling, a model which interpolates between the Fermi liquid and the Mott insulating phases.

International Journal of Modern Physics B•Jun 30, 1993•0 citations

Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons

P. J. H. Denteneer

A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral t over on-site interaction U, but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in t/U. For the energy the expansion is found to have an accuracy of better than 1% for U/t\ensuremath{\ge}8. A comparison is given with an earlier perturbation expansion based on the linear-spin-wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9601065•Physical review. B, Condensed matter•Apr 15, 1996•3 citations

Evolution of the spectrum of the Hubbard model with filling

Sherman

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion.The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators.For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions and nearest-neighbor hopping.With decreasing the electron concentration in addition to the four bands observed at half-filling, a narrow band arises near the Fermi level.The dispersion of the new band, its bandwidth and the variation with filling are close to those of the spin-polaron band in the t-J model.

arXiv:cond-mat/0602537•Condensed Matter Physics•Jan 1, 2006•1 citation
A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each vertex the problem splits into the subspaces with vacuum states'' determined by the diagonal Hubbard operators and only excitations around these vacuum states are allowed. The rules to construct diagrams are proposed. In the limit of infinite spatial dimensions the total auxiliary single-site problem exactly splits into subspaces that allows to build an analytical thermodynamically consistent approach for a Hubbard model. Some analytical results are given for the simple approximations when the two-pole (alloy-analogy solution) and four-pole (Hartree-Fock approximation) structure for Green's function is obtained. Two poles describe contribution from the Fermi-liquid component, which is dominant for small electron and hole concentrations (overdoped case'' of high-Tc′s),{T}_{c}'\mathrm{s}),Tc′​s), whereas other two describe contribution from the non-Fermi liquid and are dominant close to half-filling (``underdoped case'').
In the limit of infinite spatial dimensions, a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction ( U < ∞ ), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different "vacuum states".Some analytical results are given for the Hartree-Fock approximation when the 4pole structure for Green's function is obtained: two poles describe contribution from the Fermi liquid component, which is ferromagnetic and dominant for small electron and hole concentrations ("overdoped case" of high-T c 's), whereas other two describe contribution from the non-Fermi liquid, which is antiferromagnetic and dominant close to half filling ("underdoped case").
We develop a perturbation expansion in the intersite hopping around the atomic limit of the Hubbard model. It is valid for arbitrary finite temperatures and interaction strengths. Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived. They reduce the calculation of any finite-order contribution to simple algebra. This opens the way for series extrapolations from computer-aided high-finite-order evaluations. Discrepancies in earlier expansions around the atomic limit are clarified. The present expansion scheme involves only connected diagrams with unrestricted lattice sums. This allows one to perform a vertex renormalization as for the linked-cluster expansion of the Ising model. The renormalized perturbation expansion can be used to construct self-consistent approximations which are automatically exact in the atomic limit. In the limit of high lattice dimensions, only fully two-particle reducible embeddings of diagrams on the lattice contribute. The single-particle properties of the infinite-dimensional Hubbard model reduce to those of independent tight-binding fermions hopping between dressed sites.
An approximate analytical scheme of the dynamical mean-field theory (DMFT), that is used for electron systems with Hubbard correlations and is exact in the limit of the infinite dimensionality of a space, is developed.The effective single-site problem arising in the framework of this method is formulated in terms of the auxiliary Fermi-field.The irreducible Green's function technique with the projecting on the Hubbard basis of Fermi-operators is used for its solution.A system of DMFT equations is obtained in the approximation which is a generalization of the Hubbard-III approximation and combines it with a self-consistent renormalization of the local electron levels.It is shown that the proposed approach includes as simple specific cases a number of known approximations (Hubbard-III, AA, MAA, . . . ) based on the assumption of the single-site structure of the electron selfenergy.
The diagrammatic formulation of the single-site approximation to the Hubbard model immediately yields the exact solution to the Falikov-Kimball model in infinite dimensions. By an extension of the alloy analogy, we then derive a two-fluid model, dividing self-consistently the electron system among itinerating and relatively localized particles. Our theory coincides with the CPA only the at half-filling and u=∞. We start by studying the mean field approximation to our theory and identify a phase boundary in the particle density-interaction strength (n−u) plane at which the Fermi liquid model breaks down. Then the effect of fluctuations in the Fermi liquid regime is considered and, finally, we construct, at half-filling, a model which interpolates between the Fermi liquid and the Mott insulating phases.
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral t over on-site interaction U, but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in t/U. For the energy the expansion is found to have an accuracy of better than 1% for U/t\ensuremath{\ge}8. A comparison is given with an earlier perturbation expansion based on the linear-spin-wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed. \textcopyright{} 1996 The American Physical Society.
The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion.The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators.For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions and nearest-neighbor hopping.With decreasing the electron concentration in addition to the four bands observed at half-filling, a narrow band arises near the Fermi level.The dispersion of the new band, its bandwidth and the variation with filling are close to those of the spin-polaron band in the t-J model.