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arXiv:0708.1765 · Physical Review B

Quantum phase transitions in the extended periodic Anderson model

Akihisa Koga, Norio Kawakami, Robert Peters, Thomas Pruschke

Published Jan 15, 2008• 24 citations
arXivHTMLPDF

Abstract

We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using the combination of dynamical mean-field theory and the numerical renormalization group. At half filling, a first-order phase transition between a Mott insulating state and a Kondo insulating state occurs in the strong-coupling regime. We furthermore find that a metallic state is stabilized in the weak-coupling regime. This state should be adiabatically connected to the orbital selective Mott state with one orbital-localized and the other itinerant. The effect of hole doping is also addressed.

DOI
10.1103/physrevb.77.045120

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We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using the combination of dynamical mean-field theory and the numerical renormalization group. At half filling, a first-order phase transition between a Mott insulating state and a Kondo insulating state occurs in the strong-coupling regime. We furthermore find that a metallic state is stabilized in the weak-coupling regime. This state should be adiabatically connected to the orbital selective Mott state with one orbital-localized and the other itinerant. The effect of hole doping is also addressed.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.
We use the numerical renormalization group method to investigate the spectral properties of a single-impurity Anderson model with a gap $\ensuremath{\delta}$ across the Fermi level in the conduction-electron spectrum. For any finite $\ensuremath{\delta}>0$, at half filling the ground state of the system is always a doublet. Away from half filling a quantum phase transition (QPT) occurs as function of the gap value $\ensuremath{\delta}$, and the system evolves from the strong-coupling (SC) Kondo-type state, corresponding to $\ensuremath{\delta}<{\ensuremath{\delta}}_{C}$ toward a localized moment (LM) regime for $\ensuremath{\delta}>{\ensuremath{\delta}}_{C}$. The opening of the gap leads to the formation of one (two) bound states when the system is in the SC (LM) regime. The evolution across the QPT of their positions and the corresponding weights together with the dynamic properties of the model are investigated.
We study the ground-state properties of an extended periodic Anderson model to understand the role of Hund's coupling between localized and itinerant electrons using the density-matrix renormalization group algorithm. By calculating the von Neumann entropies we show that two phase transitions occur and two new phases appear as the hybridization is increased in the symmetric half-filled case due to the competition between Kondo effect and Hund's coupling. In the intermediate phase, which is bounded by two critical points, we found a dimerized ground state, while in the other spatially homogeneous phases the ground state is Haldane-like and Kondo-singlet-like, respectively. We also determine the entanglement spectrum and the entanglement diagram of the system by calculating the mutual information thereby clarifying the structure of each phase.
Abstract The Mott transition is a paradigmatic phenomenon where Coulomb interactions between electrons drive a metal‐insulator phase transition. It is extensively studied within the Hubbard model, where a quantum critical transition occurs at a finite temperature second‐order critical point. This work investigates the Mott transition in a modified periodic Anderson model that may be viewed as a three‐orbital lattice model including an interacting, localized orbital coupled to a delocalized conduction orbital via a second conduction orbital. Within the dynamical mean field theory, this model possesses a strictly zero temperature quantum critical point separating a Fermi liquid and a Mott insulating phase. By employing a simplified version of the dynamical mean field theory, namely, the two‐site or linearized dynamical mean field theory, an analytical estimate is provided for the critical parameter strengths at which the transition occurs at zero temperature. An analytical estimate of the single‐site von Neumann entanglement entropy is also provided. This measure can be used as a robust identifier for the phase transition. These calculations are extended to their cluster version to incorporate short‐range, spatial correlations and discuss their effects on the transition observed in this model.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.