Application of Gutzwiller's Variational Method to the Metal-Insulator Transition
TL;DR: In this article, it was shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom.
Abstract: It is shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom. The susceptibility and effective mass are calculated in the metallic phase and are found to be enhanced by a common factor which diverges at the critical value of the interaction.
Citations
More filters
TL;DR: The dynamical mean field theory of strongly correlated electron systems is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
Abstract: We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.
5,230 citations
TL;DR: In this paper, a new approach to correlated Fermi systems such as the Hubbard model, the periodic Anderson model etc. is discussed, which makes use of the limit of high spatial dimensions.
Abstract: A new approach to correlated Fermi systems such as the Hubbard model, the periodic Anderson model etc. is discussed, which makes use of the limit of high spatial dimensions. This limit — which is wellknown in the case of classical as well as localized quantum spin models — is found to be very helpful also in the case of quantum mechanical models with itinerant degrees of freedom. Many investigations, which are prohibitively difficult in lower dimensions, become tractable in this limit. In particular, essential features of systems in d = 3, and even lower dimensions, are very well described by the results in d = ∞ or expansions around this limit. A brief review of the state-of-the-art is presented.
1,605 citations
TL;DR: The electronic properties of a prototypical correlated insulator vanadium dioxide in which the metallic state can be induced by increasing temperature is reported, setting the stage for investigations of charge dynamics on the nanoscale in other inhomogeneous correlated electron systems.
Abstract: Electrons in correlated insulators are prevented from conducting by Coulomb repulsion between them. When an insulator-to-metal transition is induced in a correlated insulator by doping or heating, the resulting conducting state can be radically different from that characterized by free electrons in conventional metals. We report on the electronic properties of a prototypical correlated insulator vanadium dioxide in which the metallic state can be induced by increasing temperature. Scanning near-field infrared microscopy allows us to directly image nanoscale metallic puddles that appear at the onset of the insulator-to-metal transition. In combination with far-field infrared spectroscopy, the data reveal the Mott transition with divergent quasi-particle mass in the metallic puddles. The experimental approach used sets the stage for investigations of charge dynamics on the nanoscale in other inhomogeneous correlated electron systems.
1,283 citations
TL;DR: In this paper, a review of the physics of spin liquid states is presented, including spin-singlet states, which may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of SU(2), U(1), or Z2.
Abstract: This is an introductory review of the physics of quantum spin liquid states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semiclassical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semiclassical approaches fail once quantum mechanics become important and then describe the alternative approaches for addressing the problem. Mainly spin-1/2 systems are discussed, and most of the time is spent in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU(2), U(1), or Z2 spin liquid states. A review is given of the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S>1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular-lattice systems [κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2], kagome-lattice system [ZnCu3(OH)6Cl2], and hyperkagome lattice system (Na4Ir3O8), is reviewed and compared against the corresponding theories.
1,108 citations
Cites background from "Application of Gutzwiller's Variati..."
...…and spin liquid states suggests an alternative picture of the Mott metal-insulator transition with respect to that put forward by Brinkman and Rice (Brinkman and Rice, 1970), who proposed that a metal-insulator (Mott) transition is characterized by a diverging effective mass m ∗ m → ∞ and an…...
[...]
...The close relationship between Fermi liquids and spin liquid states suggests an alternative picture of the Mott metal-insulator transition with respect to that put forward by Brinkman and Rice (Brinkman and Rice, 1970), who proposed that a metal-insulator (Mott) transition is characterized by a diverging effective mass m ∗ m → ∞ and an inverse compressibility κ → 0 at the Mott transition point, with a correspondingly vanishing quasi-particle renormalization weight Z ∼ mm∗ → 0....
[...]
TL;DR: A tentative theory is proposed to combine various features of the problem which have been revealed by some of the different approaches to the theory of noninteracting electrons in a static disordered lattice.
1,084 citations