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 and the Landau Fermi-liquid parameter of the Hubbard model and the three-band CuO2 model

Hiroyuki Kaga, Taiichirou Saikawa, Chihiro Ohmori

Published Jul 1, 1996• 1 citation
Publisher

Abstract

Magnetic susceptibilities of interacting (d) electrons in the Hubbard model and the three-band ${\mathrm{CuO}}_{2}$ model are worked out within the Gaussian fluctuations of the functional integral in the slave boson representation. The normalized Landau Fermi-liquid parameter |${\mathit{F}}_{0}^{\mathit{a}}$|/\ensuremath{\alpha} (\ensuremath{\alpha}\ensuremath{\equiv}${\mathit{W}}_{0}$${\mathit{N}}_{\mathit{F}}^{0}$, ${\mathit{N}}_{\mathit{F}}^{0}$ the density of states at the Fermi level, and ${\mathit{W}}_{0}$ the bare bandwidth) defined from the susceptibility expression is investigated for the two models as functions of Coulomb repulsion U, charge-transfer energy \ensuremath{\Delta}, and doping concentration \ensuremath{\delta}. It is shown that the Landau parameter for the three-band model is larger and exhibits different renormalization behaviors than that for the Hubbard model in both the weak- and strong-coupling regimes except in the Mott-Hubbard weak-coupling regime, where it takes the same random-phase approximation form U/${\mathit{W}}_{0}$ as the latter. The reasons for these results are analyzed. The slave-boson Landau parameter for the Hubbard model exactly reproduces the T-matrix expression |${\mathit{F}}_{0}^{\mathit{a}}$|/\ensuremath{\alpha}=U/${\mathit{W}}_{0}$/(1+U/${\mathit{W}}_{0}$) in the low-density limit, whose renormalization has the different origin from that in the dilutely doped regime. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.1342

Related papers

Quantum Monte Carlo Simulations and Weak-Coupling Approximations for the Three-Band Hubbard Model

R. Putz, H. Endres, A. Muramatsu +1 more

We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.

Notes on numerical fluid mechanics•Jan 1, 1994•1 citation

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

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

QUANTUM MONTE CARLO SIMULATIONS FOR THE THREE-BAND HUBBARD MODEL

G. Dopf, Alejandro Muramatsu, Werner R. Hanke

We present in this article results of Quantum Monte Carlo simulations for the three-band Hubbard model obtained both with the grand canonical approach as well as with the T =0 formalism. A direct comparison of Quantum Monte Carlo results with experimental values for the charge-transfer gap leads to a set of parameters for the three-band Hubbard model that consistently describes salient features of the high- T c superconductors. We find long-range antiferromagnetic order in the undoped case as well as an incommensurate structure for a doping concentration of δ≈0.20. Moreover the magnetic susceptibility as a function of doping δ is in a qualitative agreement with experiments. Concerning dynamical properties, we have evaluated the spectral density [Formula: see text]. The dispersion of the state with the lowest excitation energy is in very good agreement with experimental photoemission and inverse photoemission experiments for a doping concentration of δ=0.25. In the superconducting regime, we find that the interaction vertex for the pairing correlation function in the extended s-channel shows a maximum for δ~0.20, resembling the dependence of T c on doping. This feature is not present for other symmetries of the order parameter or in other parameter regions.

International Journal of Modern Physics C•Feb 1, 1992•2 citations

Strongly Correlated Fermi Liquid and the Normal State of High Tc Superconductors

Ziqiang Wang

New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.

International Journal of Modern Physics B•Mar 1, 1992•18 citations

Finite-Uslave-boson methods and the intersite magnetic correlations in the Hubbard models

Hiroyuki Kaga

We examine the two existing slave-boson methods for the finite-U Hubbard model by Kotliar and Ruckenstein (KR) and by Newns et al. and Zou and Anderson (NZA) in the light of the Fermi-liquid quasiparticle picture. It is shown that to treat doubly occupied states the KR slave-boson scheme is more consistent with this picture and that the well-known erroneous gauge-symmetry breaking encountered in the mean-field treatment of the NZA double-occupancy boson is due to the presence of the hidden double-fermion operators. Then, the effective intersite antiferromagnetic interaction between quasiparticles is derived in the KR slave-boson approach by taking into account empty and double-occupancy slave-boson fluctuations to O(1/${\mathit{N}}^{2}$) in the 1/N expansion of the functional-integral formalism. The obtained effective exchange coupling constant ${\mathit{J}}_{\mathrm{eff}}$(\ensuremath{\delta})=J(2${\mathit{p}}_{0}^{2}$-\ensuremath{\delta}/2) with J\ensuremath{\equiv}${\mathit{t}}_{\mathit{i}\mathit{j}}^{2}$/U is strongly dependent upon doping \ensuremath{\delta} and is scaled with the reduced Coulomb repulsion u\ensuremath{\equiv}U/${\mathit{U}}_{\mathit{c}}$ in the two-dimensional (2D) and 3D Hubbard models, where ${\mathit{U}}_{\mathit{c}}$ is the critical value for the metal-to-insulator transition. The roles of this intersite correlation and the spin-dependent band-renormalization correlation included in the mean-field theory for the paramagnetic-to-antiferromagnetic instability are compared in the two Hubbard models. The intersite contribution is more significant in the 2D case than in the 3D case, but is generally small compared with the band effect except for small dopings \ensuremath{\delta} and smaller U values. The maximum doping ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$ for the paramagnetic-to-ferromagnetic instability in the strong-coupling limit (U\ensuremath{\rightarrow}\ensuremath{\infty}) of the 2D and 3D Hubbard models is found to be ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.28 and ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.38, respectively.

Physical review. B, Condensed matter•Jul 15, 1992•8 citations
Magnetic susceptibilities of interacting (d) electrons in the Hubbard model and the three-band CuO2{\mathrm{CuO}}_{2}CuO2​ model are worked out within the Gaussian fluctuations of the functional integral in the slave boson representation. The normalized Landau Fermi-liquid parameter |F0a{\mathit{F}}_{0}^{\mathit{a}}F0a​|/\ensuremath{\alpha} (\ensuremath{\alpha}\ensuremath{\equiv}{\mathit{W}}_{0}$${\mathit{N}}_{\mathit{F}}^{0}, NF0{\mathit{N}}_{\mathit{F}}^{0}NF0​ the density of states at the Fermi level, and W0{\mathit{W}}_{0}W0​ the bare bandwidth) defined from the susceptibility expression is investigated for the two models as functions of Coulomb repulsion U, charge-transfer energy \ensuremath{\Delta}, and doping concentration \ensuremath{\delta}. It is shown that the Landau parameter for the three-band model is larger and exhibits different renormalization behaviors than that for the Hubbard model in both the weak- and strong-coupling regimes except in the Mott-Hubbard weak-coupling regime, where it takes the same random-phase approximation form U/W0{\mathit{W}}_{0}W0​ as the latter. The reasons for these results are analyzed. The slave-boson Landau parameter for the Hubbard model exactly reproduces the T-matrix expression |F0a{\mathit{F}}_{0}^{\mathit{a}}F0a​|/\ensuremath{\alpha}=U/W0{\mathit{W}}_{0}W0​/(1+U/W0{\mathit{W}}_{0}W0​) in the low-density limit, whose renormalization has the different origin from that in the dilutely doped regime. \textcopyright{} 1996 The American Physical Society.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
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.
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 present in this article results of Quantum Monte Carlo simulations for the three-band Hubbard model obtained both with the grand canonical approach as well as with the T =0 formalism. A direct comparison of Quantum Monte Carlo results with experimental values for the charge-transfer gap leads to a set of parameters for the three-band Hubbard model that consistently describes salient features of the high- T c superconductors. We find long-range antiferromagnetic order in the undoped case as well as an incommensurate structure for a doping concentration of δ≈0.20. Moreover the magnetic susceptibility as a function of doping δ is in a qualitative agreement with experiments. Concerning dynamical properties, we have evaluated the spectral density [Formula: see text]. The dispersion of the state with the lowest excitation energy is in very good agreement with experimental photoemission and inverse photoemission experiments for a doping concentration of δ=0.25. In the superconducting regime, we find that the interaction vertex for the pairing correlation function in the extended s-channel shows a maximum for δ~0.20, resembling the dependence of T c on doping. This feature is not present for other symmetries of the order parameter or in other parameter regions.
New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.
We examine the two existing slave-boson methods for the finite-U Hubbard model by Kotliar and Ruckenstein (KR) and by Newns et al. and Zou and Anderson (NZA) in the light of the Fermi-liquid quasiparticle picture. It is shown that to treat doubly occupied states the KR slave-boson scheme is more consistent with this picture and that the well-known erroneous gauge-symmetry breaking encountered in the mean-field treatment of the NZA double-occupancy boson is due to the presence of the hidden double-fermion operators. Then, the effective intersite antiferromagnetic interaction between quasiparticles is derived in the KR slave-boson approach by taking into account empty and double-occupancy slave-boson fluctuations to O(1/N2{\mathit{N}}^{2}N2) in the 1/N expansion of the functional-integral formalism. The obtained effective exchange coupling constant Jeff{\mathit{J}}_{\mathrm{eff}}Jeff​(\ensuremath{\delta})=J(2p02{\mathit{p}}_{0}^{2}p02​-\ensuremath{\delta}/2) with J\ensuremath{\equiv}tij2{\mathit{t}}_{\mathit{i}\mathit{j}}^{2}tij2​/U is strongly dependent upon doping \ensuremath{\delta} and is scaled with the reduced Coulomb repulsion u\ensuremath{\equiv}U/Uc{\mathit{U}}_{\mathit{c}}Uc​ in the two-dimensional (2D) and 3D Hubbard models, where Uc{\mathit{U}}_{\mathit{c}}Uc​ is the critical value for the metal-to-insulator transition. The roles of this intersite correlation and the spin-dependent band-renormalization correlation included in the mean-field theory for the paramagnetic-to-antiferromagnetic instability are compared in the two Hubbard models. The intersite contribution is more significant in the 2D case than in the 3D case, but is generally small compared with the band effect except for small dopings \ensuremath{\delta} and smaller U values. The maximum doping ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$ for the paramagnetic-to-ferromagnetic instability in the strong-coupling limit (U\ensuremath{\rightarrow}\ensuremath{\infty}) of the 2D and 3D Hubbard models is found to be ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.28 and ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.38, respectively.