The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.

arXiv:0707.0142Jul 2, 20072 citations

The Metal-Insulator Transition in the Hubbard Model

M. G. Zacher, Ansgar Dorneich, C. Gröber +2 more

Springer eBooksJan 1, 20001 citation

Metal-insulator transition in the Hubbard model

R. Bulla, Thomas Pruschke, Alex C. Hewson

Physica B Condensed MatterJan 1, 19999 citations

Mott-Hubbard transition in the mass-imbalanced Hubbard model

Marie-Therese Philipp, Markus Wallerberger, Patrik Gunacker +1 more

The mass-imbalanced Hubbard model represents a continuous evolution from the Hubbard to the Falicov-Kimball model. We employ dynamical mean field theory and study the paramagnetic metal-insulator transition, which has a very different nature for the two limiting models. Our results indicate that the metal-insulator transition rather resembles that of the Hubbard model as soon as a tiny hopping between the more localized fermions is switched on. At low temperatures we observe a first-order metal-insulator transition and a three peak structure. The width of the central peak is the same for the more and less mobile fermions when approaching the phase transition, which agrees with our expectation of a common Kondo temperature and phase transition for the two species.The mass-imbalanced Hubbard model represents a continuous evolution from the Hubbard to the Falicov-Kimball model. We employ dynamical mean field theory and study the paramagnetic metal-insulator transition, which has a very different nature for the two limiting models. Our results indicate that the metal-insulator transition rather resembles that of the Hubbard model as soon as a tiny hopping between the more localized fermions is switched on. At low temperatures we observe a first-order metal-insulator transition and a three peak structure. The width of the central peak is the same for the more and less mobile fermions when approaching the phase transition, which agrees with our expectation of a common Kondo temperature and phase transition for the two species.

arXiv:1611.10079The European Physical Journal BJun 1, 201710 citations

The Metal Insulator Transition in the Hubbard Model

E. V. Anda

NATO ASI series. Series B : PhysicsJan 1, 19951 citation

Local theory for Mott-Anderson localization

Sudeshna Sen, Hanna Terletska, Juana Moreno +2 more

The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a nonperturbative local moment approach within the framework of dynamical mean-field theory with a typical medium. Our focus is on the breakdown of the metallic phase near the metal-insulators transition as seen in the single-particle spectra, scattering rates, and the associated distribution of Kondo scales. We demonstrate the emergence of a universal, underlying low-energy scale, ${T}_{K}^{\mathrm{peak}}$ . This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies $\ensuremath{\omega}\ensuremath{\lesssim}{T}_{K}^{\mathrm{peak}}$ display Fermi liquid universality crossing over to an incoherent universal dynamics for $\ensuremath{\omega}\ensuremath{\gg}{T}_{K}^{\mathrm{peak}}$ in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low-energy physics is governed by an effective, disorder renormalized Kondo screening.The paramagnetic metallic phase of the Anderson-Hubbard model (AHM) is investigated using a nonperturbative local moment approach within the framework of dynamical mean-field theory with a typical medium. Our focus is on the breakdown of the metallic phase near the metal-insulators transition as seen in the single-particle spectra, scattering rates, and the associated distribution of Kondo scales. We demonstrate the emergence of a universal, underlying low-energy scale, ${T}_{K}^{\mathrm{peak}}$. This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies $\ensuremath{\omega}\ensuremath{\lesssim}{T}_{K}^{\mathrm{peak}}$ display Fermi liquid universality crossing over to an incoherent universal dynamics for $\ensuremath{\omega}\ensuremath{\gg}{T}_{K}^{\mathrm{peak}}$ in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low-energy physics is governed by an effective, disorder renormalized Kondo screening.

arXiv:1608.04357Physical review. B./Physical review. BDec 2, 201616 citations

{T}_{K}^{\mathrm{peak}}

. This lies close to the peak of the distribution of Kondo scales obtained within the metallic phase of the paramagnetic AHM. Spectral dynamics for energies $\ensuremath{\omega}\ensuremath{\lesssim}{T}_{K}^{\mathrm{peak}}$ display Fermi liquid universality crossing over to an incoherent universal dynamics for $\ensuremath{\omega}\ensuremath{\gg}{T}_{K}^{\mathrm{peak}}$ in the scaling regime. Such universal dynamics indicate that within a local theory the low to moderately low-energy physics is governed by an effective, disorder renormalized Kondo screening.