Using second-order perturbation theory in U for the self-energy, we solve the self-consistent equations for the local Green function of the infinite-dimensional Hubbard model. We consider the cases of Gaussian and semicircular free densities of states (DOS), and calculate the spectral densities rho(omega) for various U. In the semicircular case we investigate the existence of a Mon transition at half-filling. Even for large U we obtain a metallic solution. Treating the free Dos as a variable parameter, the method also gives an approximate solution of the finite-dimensional Hubbard model. We consider the case of a (regularized) logarithmic Dos appropriate for the two-dimensional case.Using second-order perturbation theory in U for the self-energy, we solve the self-consistent equations for the local Green function of the infinite-dimensional Hubbard model. We consider the cases of Gaussian and semicircular free densities of states (DOS), and calculate the spectral densities rho(omega) for various U. In the semicircular case we investigate the existence of a Mon transition at half-filling. Even for large U we obtain a metallic solution. Treating the free Dos as a variable parameter, the method also gives an approximate solution of the finite-dimensional Hubbard model. We consider the case of a (regularized) logarithmic Dos appropriate for the two-dimensional case.

Sep 10, 20260 citations

Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique

A. Sherman

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion Uc ≈ 6.96t, where t is the hopping constant. The calculated spectral functions, density of states (DOS) and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for U > Uc and for temperatures, at which magnetic ordering and spin correlations are suppressed. For U < Uc and lower temperatures the theory describes qualitatively correctly the positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of δ-function peaks in the Hubbard-I approximation.The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion Uc ≈ 6.96t, where t is the hopping constant. The calculated spectral functions, density of states (DOS) and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for U > Uc and for temperatures, at which magnetic ordering and spin correlations are suppressed. For U < Uc and lower temperatures the theory describes qualitatively correctly the positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of δ-function peaks in the Hubbard-I approximation.

arXiv:1410.8289International Journal of Modern Physics BApr 15, 20158 citations

Physical properties of the half-filled Hubbard model in infinite dimensions

Antoine Georges, Werner Krauth

A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported.A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported.

Physical review. B, Condensed matterSep 1, 1993235 citations

The metal-insulator transition and Fermi-liquid behaviour in the infinite-dimensional Hubbard model

S. Wermbter, G. Czycholl

We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.

Journal of Physics Condensed MatterJul 11, 199415 citations

Quasi-Particle Density of States of Two-Dimensional Hubbard Model

Takashi Hotta

The density of states (DOS) of the two-dimensional Hubbard model is calculated in second-order perturbation with respect to the on-site Coulomb interaction U . The direct analytic continuation formula is presented to calculate the self-energy on the real-frequency axis. The momentum as well as the energy integral in the self-energy is seriously carried out with use of the Fast-Fourier-Transformation algorithm. Near the half-filling, the imaginary part of the self-energy becomes proportional to the energy in the vicinity of the Fermi level in our weak-coupling calculation. In the interacting case, the van Hove singularity (VHS) in DOS is smeared by the self-energy effect, but there still exists a sharp peak structure due to VHS.The density of states (DOS) of the two-dimensional Hubbard model is calculated in second-order perturbation with respect to the on-site Coulomb interaction U . The direct analytic continuation formula is presented to calculate the self-energy on the real-frequency axis. The momentum as well as the energy integral in the self-energy is seriously carried out with use of the Fast-Fourier-Transformation algorithm. Near the half-filling, the imaginary part of the self-energy becomes proportional to the energy in the vicinity of the Fermi level in our weak-coupling calculation. In the interacting case, the van Hove singularity (VHS) in DOS is smeared by the self-energy effect, but there still exists a sharp peak structure due to VHS.

Journal of the Physical Society of JapanAug 15, 19956 citations

Equation-of-motion approach to the Hubbard model in infinite dimensions

Claudius Gros

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, ${\mathit{G}}^{(\mathit{n})}$ (\ensuremath{\omega}), n=2,3,.... The first n-1 equations of motion are exactly fullfilled by ${\mathit{G}}^{(\mathit{n})}$ (\ensuremath{\omega}) and the nth equation of motion is decoupled following a simple set of decoupling rules. ${\mathit{G}}^{(2)}$ (\ensuremath{\omega}) corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for n=2,3,4.We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, ${\mathit{G}}^{(\mathit{n})}$(\ensuremath{\omega}), n=2,3,.... The first n-1 equations of motion are exactly fullfilled by ${\mathit{G}}^{(\mathit{n})}$(\ensuremath{\omega}) and the nth equation of motion is decoupled following a simple set of decoupling rules. ${\mathit{G}}^{(2)}$(\ensuremath{\omega}) corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for n=2,3,4.

arXiv:cond-mat/9403030Physical review. B, Condensed matterSep 15, 199429 citations

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function,

{\mathit{G}}^{(\mathit{n})}

(\ensuremath{\omega}), n=2,3,.... The first n-1 equations of motion are exactly fullfilled by

{\mathit{G}}^{(\mathit{n})}

(\ensuremath{\omega}) and the nth equation of motion is decoupled following a simple set of decoupling rules.

{\mathit{G}}^{(2)}

(\ensuremath{\omega}) corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for n=2,3,4.