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

International Journal of Modern Physics B

Study of the Large-Dimensional Hubbard Model Via a New Nonperturbative Method

Jongbae Hong, Jinsook Song

Published Nov 10, 1998• 0 citations
Publisher

Abstract

A new nonperturbative method calculating the one-particle Green's function is introduced and applied to the Hubbard model. We show the metal–insulator transition in the paramagnetic ground state of the half-filled Hubbard model on a Bethe lattice with infinite connectivity. This method describes the transition regime appropriately. The analytic result using the continued fraction formalism which has a close relationship with present formalism is provided for comparison. As for the Hubbard model with doping, we obtain the optical conductivities and show the interesting features, such as midinfrared band and isobestic point. We also show that the sharp frequency-dependent behavior at large doping is the dispersed Drude type in this model.

DOI
10.1142/s0217979298001642

Related papers

A Nonperturbative Approach to One-Particle Green's Function

Jongbae Hong

A nonperturbative method to obtain on- and off-site one-particle Green's function is introduced and applied to noninteracting Hubbard model with next nearest neighbor hopping and interacting Hubbard model in large dimensions, for example. The former gives some lessons on the method and shows the advantage of the method compared with continued fraction formalism. The latter is treated by selecting important dynamic processes contributing to the Green's function when correlation is strong. We consider the model in the Bethe lattice with large connectivity. The dynamic processes describing on-site spin fluctuation clearly shows metal-insulator transition in the paramagnetic ground state at half filling.

arXiv:cond-mat/9709087•Sep 8, 1997•0 citations

Analytic treatment of Mott-Hubbard transition in the half-filled Hubbard model and its thermodynamics

Jongbae Hong, Hae‐Young Kee

The Mott-Hubbard transition in the half-filled Hubbard model is studied analytically on a Bethe lattice for the paramagnetic state and the classical N\'eel state. The single-particle density of states is obtained by calculating the one-particle Green's function represented by the Lanczos infinite continued fraction. The paramagnetic solution shows that the Mott-Hubbard transition is signaled by both collapsing Hubbard bands at ${\mathit{U}}_{\mathit{c}}$=2${\mathit{t}}_{\mathrm{*}}$ and a sharp Lorentzian peak appearing at midgap at U${\mathit{U}}_{\mathit{c}}$. For the N\'eel state, however, the system becomes an insulator for U>0. We also obtain the specific heat and entropy for both the metallic and insulating regimes. Our analytic work reproduces the key results obtained by numerical method in infinite dimensions.

arXiv:cond-mat/9501077•Physical review. B, Condensed matter•Jul 15, 1995•20 citations

On the Magnetic and Metal-Insulator Transitions in a Two-Dimensional Hubbard Model

Hisashi Kondo, Tôru Moriya

Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.

Journal of the Physical Society of Japan•Jan 15, 1998•4 citations

Transition characteristics of a Mott-Hubbard system in large dimensions

Jongbae Hong, Tae‐Suk Kim

We study the nature of metal-insulator transition in the paramagnetic state for the Hubbard model on the Bethe lattice. The single-particle density of states is calculated via the operator Lanczos method. Our study shows that the metal-insulator transition is continuous and there is no preformed gap. The quasiparticle weight vanishes linearly with the distance from the transition point ${(U}_{c})$ in agreement with results of iterative perturbation theory and exact diagonalization method. Our ${U}_{c}$ is comparable to that by the random dispersion approximation. Our result indicates non-Fermi-liquid feature at the transition point.

Physical review. B, Condensed matter•Nov 15, 2000•1 citation

Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model

Heinz J. Schulz

The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2${\mathit{k}}_{\mathit{F}}$x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$ ${\mathrm{ln}}^{1/2}$(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.

Physical Review Letters•Jun 4, 1990•652 citations

Optical properties of one- and two-dimensional Hubbard andt-Jmodels

W. Stephan, Peter Horsch

The optical conductivity for the Hubbard and t-J models is calculated numerically by use of a Lanczos algorithm. One- and two-dimensional systems of up to 16 sites with periodic and open boundary conditions are examined for the t-J model, as well as Hubbard-model systems of up to 9 sites. In the one-dimensional case, the low-frequency part of the conductivity away from half filling is shown to consist almost entirely of a single \ensuremath{\delta} function (Drude peak) even for J of the order of t. This is a direct consequence of the decoupling of charge and spin in one dimension. In two dimensions there is an additional broad absorption band above the Drude peak, consistent with the experimentally observed midinfrared band in the copper oxide superconductors. The importance of vertex corrections is demonstrated by comparing the exact conductivity with the convolution integral of the exact single-particle Green's function.

Physical review. B, Condensed matter•Nov 1, 1990•134 citations
A new nonperturbative method calculating the one-particle Green's function is introduced and applied to the Hubbard model. We show the metal–insulator transition in the paramagnetic ground state of the half-filled Hubbard model on a Bethe lattice with infinite connectivity. This method describes the transition regime appropriately. The analytic result using the continued fraction formalism which has a close relationship with present formalism is provided for comparison. As for the Hubbard model with doping, we obtain the optical conductivities and show the interesting features, such as midinfrared band and isobestic point. We also show that the sharp frequency-dependent behavior at large doping is the dispersed Drude type in this model.
A nonperturbative method to obtain on- and off-site one-particle Green's function is introduced and applied to noninteracting Hubbard model with next nearest neighbor hopping and interacting Hubbard model in large dimensions, for example. The former gives some lessons on the method and shows the advantage of the method compared with continued fraction formalism. The latter is treated by selecting important dynamic processes contributing to the Green's function when correlation is strong. We consider the model in the Bethe lattice with large connectivity. The dynamic processes describing on-site spin fluctuation clearly shows metal-insulator transition in the paramagnetic ground state at half filling.
The Mott-Hubbard transition in the half-filled Hubbard model is studied analytically on a Bethe lattice for the paramagnetic state and the classical N\'eel state. The single-particle density of states is obtained by calculating the one-particle Green's function represented by the Lanczos infinite continued fraction. The paramagnetic solution shows that the Mott-Hubbard transition is signaled by both collapsing Hubbard bands at Uc{\mathit{U}}_{\mathit{c}}Uc​=2t∗{\mathit{t}}_{\mathrm{*}}t∗​ and a sharp Lorentzian peak appearing at midgap at UUc{\mathit{U}}_{\mathit{c}}Uc​. For the N\'eel state, however, the system becomes an insulator for U>0. We also obtain the specific heat and entropy for both the metallic and insulating regimes. Our analytic work reproduces the key results obtained by numerical method in infinite dimensions.
Antiferromagnetic and metal to insulator transitions in the ground state of two-dimensional half-filled and nearly half-filled Hubbard models with the nearest neighbor and the second nearest neighbor transfers (- t and t ′ , respectively) are studied by using the Green's function approach with the self-energy up to the second order in the coupling constant U . For a choice of the parameter value t ′ / t =0.2 the half-filled model undergoes the first order phase transition between paramagnetic metallic (PM) phase and antiferromagnetic insulator (AFI) phase at U / t =4.0 while the first order transition between PM and antiferromagnetic metallic (AFM) phases takes place for nearly half-filled band. The one-electron spectral density is calculated for the PM, AFM, and AFI phases near the phase boundaries. In the PM phase the quasi-particle dispersion indicates the band narrowing from the Hartree-Fock results and the flat band behavior as was indicated by previous stadies and was observed in high- T c cuprates. The quasi-particle dispersion in the AFM phase is seen to be close to the Hartree-Fock results.
We study the nature of metal-insulator transition in the paramagnetic state for the Hubbard model on the Bethe lattice. The single-particle density of states is calculated via the operator Lanczos method. Our study shows that the metal-insulator transition is continuous and there is no preformed gap. The quasiparticle weight vanishes linearly with the distance from the transition point (Uc){(U}_{c})(Uc​) in agreement with results of iterative perturbation theory and exact diagonalization method. Our Uc{U}_{c}Uc​ is comparable to that by the random dispersion approximation. Our result indicates non-Fermi-liquid feature at the transition point.
The long-distance decay of correlation functions in the one-dimensional Hubbard model is determined for arbitrary band filling and correlation strength, using the exact solution of Lieb and Wu. In particular, for either infinitely strong on-site repulsion U, or in the close proximity of half filling for any U, spin-spin correlations decay like cos(2kF{\mathit{k}}_{\mathit{F}}kF​x)${\mathit{x}}^{\mathrm{\ensuremath{-}}3/2}$ ln1/2{\mathrm{ln}}^{1/2}ln1/2(x). For infinite U the results are generalized to the case of nonzero nearest-neighbor interaction. The behavior of the frequency-dependent conductivity is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half and quarter filling.
The optical conductivity for the Hubbard and t-J models is calculated numerically by use of a Lanczos algorithm. One- and two-dimensional systems of up to 16 sites with periodic and open boundary conditions are examined for the t-J model, as well as Hubbard-model systems of up to 9 sites. In the one-dimensional case, the low-frequency part of the conductivity away from half filling is shown to consist almost entirely of a single \ensuremath{\delta} function (Drude peak) even for J of the order of t. This is a direct consequence of the decoupling of charge and spin in one dimension. In two dimensions there is an additional broad absorption band above the Drude peak, consistent with the experimentally observed midinfrared band in the copper oxide superconductors. The importance of vertex corrections is demonstrated by comparing the exact conductivity with the convolution integral of the exact single-particle Green's function.