Zero Temperature Metal-Insulator Transition in the Infinite-Dimensional Hubbard Model

Abstract

The zero-temperature transition from a paramagnetic metal to a paramagnetic insulator is investigated in the dynamical mean field theory for the Hubbard model. The self-energy of the effective impurity Anderson model (on which the Hubbard model is mapped ) is calculated using Wilson's numerical renormalization group method. Results for the quasiparticle weight, the spectral function, and the self-energy are discussed for the Bethe and the hypercubic lattice. In both cases, the metal-insulator transition is found to occur via the vanishing of a quasiparticle resonance that appears to be isolated from the Hubbard bands. PACS numbers: 71.10.Fd, 71.27. + a, 71.30. + h The Mott-Hubbard metal-insulator transition [1,2] is one of the most fascinating phenomena of strongly correlated electron systems. This transition from a paramagnetic metal to a paramagnetic insulator is found in various transition metal oxides, such as V 2 O 3 doped with Cr [3]. The mechanism driving the Mott-Hubbard transition is believed to be the local Coulomb repulsion U between electrons on a same lattice site, although the details of the transition should also be influenced by lattice degrees of freedom. Therefore, the simplest model to investigate the correlation driven metal-insulator transition is the Hubbard model(1) where c y is ͑c is ͒ denote creation (annihilation) operators for a fermion on site i, t is the hopping matrix element, and the sum P ͗ij͘ is restricted to nearest neighbors. Despite its simple structure, the solution of this model turns out to be an extremely difficult many-body problem. The situation is particularly complicated near the metalinsulator transition, where U and the bandwidth are roughly of the same order and perturbative schemes (in U or t) are not applicable.With the recent development of the dynamical mean field theory (DMFT) [7-9] a very detailed analysis of the phase diagram of the infinite-dimensional Hubbard model became possible. The iterative perturbation theory (IPT) results of [9] gave a first order metal-insulator transition at finite temperatures. The transition occurs within a coexistence region of metallic and insulating solutions extending from T 0 up to T ‫ء‬ ഠ 0.02W (W : bandwidth). On approaching the metal-insulator transition from the metallic side (i.e., on increasing U), the authors of [9] found a quasiparticle peak with vanishing spectral weight which becomes isolated from the upper and lower Hubbard bands. A consequence of this result is that the opening of the gap and the vanishing of the quasiparticle peak do not happen at the same critical U. The possibility of this scenario was questioned by various authors [2,10-12]. The criticism is partly based on the fact that the IPT is essentially a second order perturbation theory in U (although iterated due to the selfconsistency appearing in the DMFT), whereas the metalinsulator transition happens at U values of the order of the bandwidth.Nonperturbative methods are clearly needed to clarify the situation. At finite temperatures, the quantum...

Dynamical Mean-Field Theory

“…This behavior has been detected experimentally by photoemission experiments [77]. Altogether, the thermodynamic transition line U c (T ) corresponding to the Mott-Hubbard MIT is found to be of first order at finite temperatures, and is associated with a hysteresis region in the interaction range U c1 < U < U c2 , where U c1 and U c2 are the interaction values at which the insulating and metallic solution, respectively, vanish [33,37,78,79,76,80]. As shown in Fig.…”

“…To solve the self-consistency equations different techniques ("impurity solvers") have been developed which are either fully numerical and "numerically exact", or semi-analytic and approximate. The numerical solvers can be divided into renormalization group techniques such as the numerical renormalization group (NRG) [37,38] and the density-matrix renormalization group (DMRG) [39], exact diagonalization (ED) [40][41][42], and methods based on the stochastic sampling of quantum and thermal averages, i.e., quantum Monte-Carlo (QMC) techniques such as the Hirsch-Fye QMC algorithm [32,43,44,33] and continuous-time (CT) QMC [45][46][47].…”

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

“…Due to its equivalence to an Anderson impurity problem a variety of approximative techniques have been employed to solve the complicated DMFT equations, such as the iterated perturbation theory (IPT) [26] and the noncrossing approximation (NCA) [27], as well as numerically exact techniques like quantum Monte-Carlo simulations (QMC) [28], exact diagonalization (ED) [29], or the numerical renormalization group (NRG) [30]. However, NRG cannot yet be used to solve the DMFT equations for multi-band models.…”

DMFT+Σ approach to disordered hubbard model

“…In the absense of disorder one of the characteristic features of Mott-Hubbard metal-insulator transition is hysteresis behavior of the density of states, appearing with the decrease of U , starting from insulating phase [6,32]. Mott insulator phase remains (meta)stable down to rather small values of U deep within the correlated metal phase and metallic phase is restored only at about U c1 /2D ≈ 1.…”

“…In the standard DMFT approximation density of states of repulsive Hubbard model at half-filling has a typical three-peak structure [5,6,32] with pretty narrow quasiparticle (central) peak at the Fermi level and rather wide upper and lower Hubbard bands situated at energies ε ∼ ±U/2. As Hubbard repulsive interaction U grows quasiparticle band narrows within the metallic phase and disappears at Mott-Hubbard metal-insulator transition at critical interaction value U c2 /2D ≈ 1.5.…”