Quantum Phase Transition in the Two-Band Hubbard Model

Abstract

The interaction between itinerant and Mott localized electronic states in strongly correlated materials is studied within dynamical mean field theory in combination with the numerical renormalization group method. A novel nonmagnetic zero temperature quantum phase transition is found in the bad-metallic orbital-selective Mott phase of the two-band Hubbard model, for values of the Hund's exchange which are relevant to typical transition metal oxides. DOI: 10.1103/PhysRevLett.99.236404 PACS numbers: 71.27.+a, 71.10.ÿw, 71.30.+h, 72.15.Qm The nature of the metal insulator transition in multicomponent systems, with competing energy scales associated with differing bandwidths and Coulomb and exchange interactions, is currently of great interest [1]. For instance, in transition metal oxides such as Ca 2ÿx Sr x RuO 4 or manganites (e.g., La 1ÿx Sr x MnO 3 ), the Coulomb interaction between weakly and strongly correlated subbands can give rise to complex phase changes as a function of temperature, pressure, or impurity concentration. An interesting aspect of such systems is the coexistence of itinerant wide band electrons with partially or completely localized narrow band electrons. This gives rise to bad-metallic behavior as observed, for example, in the resistivity of the paramagnetic phases of VO 2 [2] and Ca 2ÿx Sr x RuO 4 at x 0:2 [3]. Even in standard Mott insulators such as V 2 O 3 and LaTiO 3 , the presence of inequivalent orbitals leads to strong orbital polarization where in the vicinity of the transition nearly localized electrons coexist with weakly itinerant bands [4 -6]. In the case of cuprates, one of the most fascinating aspects is the coexistence of strongly and weakly correlated regions of the Brillouin zone, giving rise to so-called hot spots and cold spots, with breakdown of Fermi-liquid behavior in the former and Fermi-liquid properties in the latter [7][8][9]. Since the momentum variation of the self-energy is associated with spatial fluctuations, an intriguing analogy exists between multisite interactions within a single band and single-site interactions among inequivalent orbitals.A simple model which captures some of the essential physics occurring in the systems mentioned above is the two-band Hubbard model consisting of narrow and wide subbands, coupled via local Coulomb energy U and Hund's exchange J [10,11]. As a result of the various energy scales contained in this model, its phase diagram turns out to be remarkably rich, as shown in detailed studies by many authors [12 -21]. These studies revealed that differing bandwidths and a finite Hund's exchange stabilize an orbital-selective Mott phase, in which the wide band itinerant electrons coexist with localized spins arising from Mott localization of the narrow band electrons. Further increase of the Coulomb energy U leads to a Mott transition in the wide band whose nature has remained unresolved for the important case of anisotropic Hund's exchange of relevance to many transition metal compounds.The aim of the present work is to identify...

Spin Freezing Transition and Non-Fermi-Liquid Self-Energy in a Three-Orbital Model

“…We have shown that this new transition is driven by an apparently new class of impurity-model phase transitions which should be classified and explored. The interplay with lattice-driven crystal field splittings and the orbitally selective Mott transition [14,15] is an open and interesting question. More generally the implications of the rich structure of the Slater-Kanamori interactions for the properties of the strongly correlated metal phase deserve further investigation.…”

“…We show that for densities per site n = 2, 3 the Mott transition occurs within or at the boundary of the frozen moment phase. As Costi and Liebsch have noted in the context of an orbitally selective Mott system, the presence of frozen moments may be expected to influence the Mott transition [15].The new phase appears for multiple orbitals, a different number of electrons than orbitals and a rotationally invariant on-site exchange U/3 > J > 0. While this situation is relevant to many compounds, it has has only recently become amenable to systematic study following the development of improved exact diagonalization [16] and efficient Monte Carlo methods [17,18].…”

“…We show that for densities per site n = 2, 3 the Mott transition occurs within or at the boundary of the frozen moment phase. As Costi and Liebsch have noted in the context of an orbitally selective Mott system, the presence of frozen moments may be expected to influence the Mott transition [15].…”

“…[4,5,6,7,8,9,10]. New physics related to the appearance of magnetic moments has been considered in the context of the orbitally selective Mott transition which may occur if the orbital degeneracy is lifted [11,12,13,14,15], but for orbitally degenerate models it seems accepted that the essential concepts of a paramagnetic metal to paramagnetic insulator transition and a strongly correlated paramagnetic metal phase can be carried over from studies of the oneband situation.In this paper we show that this assumption is not correct. We use the single-site dynamical mean field approximation to demonstrate the existence of a quantum phase transition between a paramagnetic Fermi liquid and an incoherent metallic phase characterized by frozen local moments (a spin-spin correlation function which does not decay to zero at long times).…”

Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

“…11 Finally, the possibility of so-called orbital-selective Mott transitions in multiband systems has been discussed extensively in the literature. 7,[12][13][14][15][16] These different trends underline the remarkably rich physics of Mott transitions in multiorbital materials.…”