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

Physical review. B, Condensed matter

Magnetic susceptibility of the strongly correlated Hubbard model

M. Bartkowiak, K. A. Chao

Published Oct 1, 1992• 5 citations
Publisher

Abstract

Using the Wick theorem for Hubbard operators, we generate the linked-cluster expansion around the atomic limit of the Hubbard model and use it to calculate the free energy, and the uniform and the staggered magnetic susceptibility up to the fourth order. We have checked all existing controversial results on this problem and found out that our results agree with those of K.-K. Pan and Y.-L. Wang [Phys. Rev. B 43, 3706 (1991)], which were derived with an entirely different method.

DOI
10.1103/physrevb.46.9228

Related papers

Magnetic susceptibility of the strongly correlated Hubbard model

Kok-Kwei Pan, Yung‐Li Wang

Using the linked-cluster expansion method, we have calculated the uniform and the staggered susceptibility of a single-band Hubbard model. We make correction of previous results of Kubo and Zhao et al.

Physical review. B, Condensed matter•Feb 1, 1991•20 citations

Linked-cluster expansion for the single-band Hubbard model

Kok-Kwei Pan, Yung‐Li Wang

Using the linked-cluster expansion, we have obtained the free energy, uniform susceptibility, and staggered susceptibility of the s-band Hubbard model to the sixth order in terms of βt, where t is the hopping integral to the nearest neighbors and β is the inverse of temperature. We show that a special technique based on the multiple-site Wick reduction theorem is more convenient than previous perturbation calculations. Our linked-cluster expansion result is for an arbitrary value of the on-site repulsion U. It has made corrections of previous results of several papers (up to fourth order) and achieved the sixth-order term.

Journal of Applied Physics•Apr 15, 1991•7 citations

Magnetic susceptibility of the Hubbard model in the strong-correlation limit

Bao-Hua Zhao, Hui‐Quan Nie, Kaiyi Zhang +2 more

Using the fourth-order perturbation expansion, we have calculated the uniform and the staggered magnetic susceptibility of the $s$-band Hubbard model. The Curie and the N\'eel temperatures are derived and the magnetic phase diagrams are constructed. Our calculation improves on the earlier work of Kubo.

Physical review. B, Condensed matter•Aug 1, 1987•22 citations

Magnetic phase diagram of the half-filled three-dimensional Hubbard model

Kok-Kwei Pan, Yung‐Li Wang

Magnetic properties of the half-filled Hubbard model on three-dimensional bipartite lattices have been studied by using the linked-cluster series expansion method. The series for the free energy and the staggered susceptibility have been calculated as a function of \ensuremath{\mathrm{B}}t for three-dimensional bipartite lattices for an arbitrary value of the Coulomb interaction U. We obtain a transition from a paramagnetic to an antiferromagnetic U/t-${\mathrm{T}}_{\mathrm{N}}$ /t phase diagram from the divergence of the staggered susceptibility series. Comparisons with Monte Carlo simulation, Onsager reaction field result of an effective spin Hamiltonian, and large-U Heisenberg high-temperature solutions are made.

Physical review. B, Condensed matter•Feb 1, 1997•5 citations

HIGH-DENSITY EXPANSION FOR THE EXTENDED HUBBARD MODEL

M. Bartkowiak

The Green’s-function diagrammatic high-density expansion technique for Hubbard’s operators is constructed and applied to the extended Hubbard model. The electron Green’s functions and the band structure of the ground state for arbitrary electron density are calculated in the zeroth-order in 1/z. The phase diagram, staggered magnetic susceptibility and the Néel temperature for the half-filled band case are derived in the first order of the high-density expansion. Connections of the high-density and linked cluster expansions are also discussed.

International Journal of Modern Physics B•Oct 1, 1987•7 citations

Correlation induced magnetic symmetry breaking

M. Bartkowiak, K. A. Chao

Using the diagrammatic technique for Hubbard operators we construct a linked-cluster perturbation expansion around the atomic limit of the Hubbard model. We first perform a computer-aided fourth-order calculation. The results clarify discrepances in earlier expansions around the large- U limit. Next, we construct a partial vertex renormalization in the second order of the linked-cluster expansion. The vertex renormalization leads to a selfconsistent magnetic symmetry breaking and allows to study explicitly magnetic oderings of the system in the whole range of temperatures and for arbitrary electron density. The presented results for the case of a half-filled energy band indicate that our approach for the Hubbard model is analogous to the mean-field theory for spin systems, and can serve as a starting point for developing advanced selfconsistent schemes which become exact in the large- U limit. We present results of a systematic numerical study of the non-half-filled-band case. In particular, the vertex-renormalized second-order calculation leads to a qualitatively correct sharp decrease of the Néel temperature as a function of concentration of holes.

Physica Scripta•Jan 1, 1992•0 citations
Using the Wick theorem for Hubbard operators, we generate the linked-cluster expansion around the atomic limit of the Hubbard model and use it to calculate the free energy, and the uniform and the staggered magnetic susceptibility up to the fourth order. We have checked all existing controversial results on this problem and found out that our results agree with those of K.-K. Pan and Y.-L. Wang [Phys. Rev. B 43, 3706 (1991)], which were derived with an entirely different method.
Using the linked-cluster expansion, we have obtained the free energy, uniform susceptibility, and staggered susceptibility of the s-band Hubbard model to the sixth order in terms of βt, where t is the hopping integral to the nearest neighbors and β is the inverse of temperature. We show that a special technique based on the multiple-site Wick reduction theorem is more convenient than previous perturbation calculations. Our linked-cluster expansion result is for an arbitrary value of the on-site repulsion U. It has made corrections of previous results of several papers (up to fourth order) and achieved the sixth-order term.
Using the fourth-order perturbation expansion, we have calculated the uniform and the staggered magnetic susceptibility of the sss-band Hubbard model. The Curie and the N\'eel temperatures are derived and the magnetic phase diagrams are constructed. Our calculation improves on the earlier work of Kubo.
Magnetic properties of the half-filled Hubbard model on three-dimensional bipartite lattices have been studied by using the linked-cluster series expansion method. The series for the free energy and the staggered susceptibility have been calculated as a function of \ensuremath{\mathrm{B}}t for three-dimensional bipartite lattices for an arbitrary value of the Coulomb interaction U. We obtain a transition from a paramagnetic to an antiferromagnetic U/t-TN{\mathrm{T}}_{\mathrm{N}}TN​ /t phase diagram from the divergence of the staggered susceptibility series. Comparisons with Monte Carlo simulation, Onsager reaction field result of an effective spin Hamiltonian, and large-U Heisenberg high-temperature solutions are made.
The Green’s-function diagrammatic high-density expansion technique for Hubbard’s operators is constructed and applied to the extended Hubbard model. The electron Green’s functions and the band structure of the ground state for arbitrary electron density are calculated in the zeroth-order in 1/z. The phase diagram, staggered magnetic susceptibility and the Néel temperature for the half-filled band case are derived in the first order of the high-density expansion. Connections of the high-density and linked cluster expansions are also discussed.
Using the diagrammatic technique for Hubbard operators we construct a linked-cluster perturbation expansion around the atomic limit of the Hubbard model. We first perform a computer-aided fourth-order calculation. The results clarify discrepances in earlier expansions around the large- U limit. Next, we construct a partial vertex renormalization in the second order of the linked-cluster expansion. The vertex renormalization leads to a selfconsistent magnetic symmetry breaking and allows to study explicitly magnetic oderings of the system in the whole range of temperatures and for arbitrary electron density. The presented results for the case of a half-filled energy band indicate that our approach for the Hubbard model is analogous to the mean-field theory for spin systems, and can serve as a starting point for developing advanced selfconsistent schemes which become exact in the large- U limit. We present results of a systematic numerical study of the non-half-filled-band case. In particular, the vertex-renormalized second-order calculation leads to a qualitatively correct sharp decrease of the Néel temperature as a function of concentration of holes.