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 Letters

Superconducting Instabilities in the Large- U Limit of a Generalized Hubbard Model

Gabriel Kotliar, Jialin Liu

Published Oct 10, 1988• 96 citations
Publisher

Abstract

We study a generalized Hubbard model in the $U=\ensuremath{\infty}$ limit with use of the slave-boson technique. The $N=\ensuremath{\infty}$ theory describes a Fermi liquid with a strongly renormalized effective mass. The $\frac{1}{N}$ corrections give rise to different superconducting instabilities depending on the band structure and the filling factor. For low densities there is a $p$-wave instability while close to half filling in the cubic lattice we find a $d$-wave instability. We also calculate Fermi-liquid parameters.

DOI
10.1103/physrevlett.61.1784

Related papers

Disorder and interactions in the Hubbard model

Gergely T. Zimányi, Elihu Abrahams

We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.

Physical Review Letters•May 28, 1990•44 citations

Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

Grégoire Lhoutellier, Raymond Frésard, Andrzej M. Oleś

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter ${F}_{0}^{a}$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism---negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at ${F}_{0}^{a}=\ensuremath{-}1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter ${F}_{0}^{s}$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to ${F}_{0}^{a}$ at $J<0$ it requires an attraction beyond a critical value ${V}_{c}$ to generate the divergence of the charge susceptibility at ${F}_{0}^{s}=\ensuremath{-}1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.

arXiv:1503.05544•Physical Review B•Jun 8, 2015•18 citations

Quasiparticle interactions in the infinite U Hubbard model.

Wei-neng Huang

The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U = $\infty$ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.

•Jan 1, 1992•0 citations

Superconductivity in the single-band hubbard model: mean-field treatment of slave-boson pairing

Thilo Kopp, F. J. Seco, Stephan Schiller +1 more

We investigate the possibility of superconductivity in the large-$U$ limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended $s$-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.

Physical review. B, Condensed matter•Dec 1, 1988•14 citations

Instabilities of the Fermi-liquid and staggered flux phases in the large-Nt-Jmodel

David C. Morse, T. C. Lubensky

We study the stability of the Fermi-liquid and staggered flux phases in the t-J model for densities off half-filling using a large-N slave-boson approach. We examine the stability of the Fermi-liquid phase with respect to flux-density-wave (FDW) and bond-density-wave (BDW), or spin-Peierls, fluctuations at arbitrary wave vector as a function of doping \ensuremath{\delta} and the ratio \ensuremath{\delta}t/J. For densities near half-filling the Fermi liquid becomes unstable below a critical ${\mathit{t}}_{\mathit{c}}$ towards an FDW state with an incommensurate wave vector k near (\ensuremath{\pi},\ensuremath{\pi}). The critical ratio \ensuremath{\delta}${\mathit{t}}_{\mathit{c}}$/J for the Fermi-liquid--FDW transition diverges rapidly as \ensuremath{\delta}\ensuremath{\rightarrow}0. For \ensuremath{\delta}>18%, the FDW instability of the Fermi liquid is preempted by a BDW instability at incommensurate k. We examine the stability of the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 staggered flux phase with respect to coupled FDW and BDW fluctuations and find that, upon lowering t/J at small \ensuremath{\delta}, the staggered flux phase remains stable for \ensuremath{\delta}t/J above a nonzero critical ratio and then develops an instability of primarily BDW character. At nonzero \ensuremath{\delta} and still lower \ensuremath{\delta}t/J, the staggered flux phase also develops an instability with respect to long-wavelength FDW fluctuations; ${\mathit{t}}_{\mathit{c}}$/J for this instability is approximately independent of \ensuremath{\delta}. We study the response function for such fluctuations analytically, showing the nontrivial k dependence induced by the presence of a small density of holes in the staggered phase. It is conjectured that this long-wavelength FDW instability is associated with the existence off half-filling of a commensurate flux phase with lower energy than the staggered flux phase.

Physical review. B, Condensed matter•May 1, 1991•23 citations

Superconductivity and incommensurate spin fluctuations in a generalized t-J model for the cuprates

C. D. Batista, L. O. Manuel, Hermenegildo Alejandro Ceccatto +1 more

We consider the slave-fermion Schwinger-boson decomposition of an effective model obtained through a systematic low-energy reduction of the three-band Hubbard Hamiltonian. The model includes a three-site term t ′′ similar to that obtained in the large- U limit of the Hubbard model but of opposite sign for realistic or large O-O hopping. For parameters close to the most realistic ones for the cuprates, the mean-field solution exhibits d + s superconductivity (predominantly d x 2 − y 2 ) with a dependence on doping x very similar to the experimentally observed. We also obtained incommensurate peaks at wave vectors ∼ π(1,1 ± 2 x ) in the spin structure factor, which also agree with experiment.

arXiv:cond-mat/9703155•Europhysics Letters (EPL)•Apr 10, 1997•22 citations
We study a generalized Hubbard model in the U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ limit with use of the slave-boson technique. The N=\ensuremath∞N=\ensuremath{\infty}N=\ensuremath∞ theory describes a Fermi liquid with a strongly renormalized effective mass. The 1N\frac{1}{N}N1​ corrections give rise to different superconducting instabilities depending on the band structure and the filling factor. For low densities there is a ppp-wave instability while close to half filling in the cubic lattice we find a ddd-wave instability. We also calculate Fermi-liquid parameters.
We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.
We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter F0a{F}_{0}^{a}F0a​ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism---negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at ${F}_{0}^{a}=\ensuremath{-}1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange JJJ and Coulomb VVV elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange J<0J<0J<0. Charge Landau parameter F0s{F}_{0}^{s}F0s​ is lowered near half filling by increasing UUU when the intersite Coulomb interaction VVV is attractive, but in contrast to F0a{F}_{0}^{a}F0a​ at J<0J<0J<0 it requires an attraction beyond a critical value Vc{V}_{c}Vc​ to generate the divergence of the charge susceptibility at ${F}_{0}^{s}=\ensuremath{-}1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.
The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U = ∞\infty∞ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.
We investigate the possibility of superconductivity in the large-UUU limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended sss-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.
We study the stability of the Fermi-liquid and staggered flux phases in the t-J model for densities off half-filling using a large-N slave-boson approach. We examine the stability of the Fermi-liquid phase with respect to flux-density-wave (FDW) and bond-density-wave (BDW), or spin-Peierls, fluctuations at arbitrary wave vector as a function of doping \ensuremath{\delta} and the ratio \ensuremath{\delta}t/J. For densities near half-filling the Fermi liquid becomes unstable below a critical tc{\mathit{t}}_{\mathit{c}}tc​ towards an FDW state with an incommensurate wave vector k near (\ensuremath{\pi},\ensuremath{\pi}). The critical ratio \ensuremath{\delta}tc{\mathit{t}}_{\mathit{c}}tc​/J for the Fermi-liquid--FDW transition diverges rapidly as \ensuremath{\delta}\ensuremath{\rightarrow}0. For \ensuremath{\delta}>18%, the FDW instability of the Fermi liquid is preempted by a BDW instability at incommensurate k. We examine the stability of the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 staggered flux phase with respect to coupled FDW and BDW fluctuations and find that, upon lowering t/J at small \ensuremath{\delta}, the staggered flux phase remains stable for \ensuremath{\delta}t/J above a nonzero critical ratio and then develops an instability of primarily BDW character. At nonzero \ensuremath{\delta} and still lower \ensuremath{\delta}t/J, the staggered flux phase also develops an instability with respect to long-wavelength FDW fluctuations; tc{\mathit{t}}_{\mathit{c}}tc​/J for this instability is approximately independent of \ensuremath{\delta}. We study the response function for such fluctuations analytically, showing the nontrivial k dependence induced by the presence of a small density of holes in the staggered phase. It is conjectured that this long-wavelength FDW instability is associated with the existence off half-filling of a commensurate flux phase with lower energy than the staggered flux phase.
We consider the slave-fermion Schwinger-boson decomposition of an effective model obtained through a systematic low-energy reduction of the three-band Hubbard Hamiltonian. The model includes a three-site term t ′′ similar to that obtained in the large- U limit of the Hubbard model but of opposite sign for realistic or large O-O hopping. For parameters close to the most realistic ones for the cuprates, the mean-field solution exhibits d + s superconductivity (predominantly d x 2 − y 2 ) with a dependence on doping x very similar to the experimentally observed. We also obtained incommensurate peaks at wave vectors ∼ π(1,1 ± 2 x ) in the spin structure factor, which also agree with experiment.