The Mott Anderson metal insulator transition in n orbital models

Florian Gebhard

Ankur Majumder, Sudeshna Sen

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.

Florian Gebhard

G. A. Canella, V. V. França

A metal can be driven to an insulating phase through distinct mechanisms. A possible way is via the Coulomb interaction, which then defines the Mott metal-insulator transition (MIT). Another possibility is the MIT driven by disorder, the so-called Anderson MIT. Here we analyze interacting particles in disordered Hubbard chains---thus comprising the Mott-Anderson physics---by investigating the ground-state entanglement with density functional theory. The localization signature on entanglement is found to be a decreasing on the entanglement degree in comparison to the clean (without interaction and disorder) case, with local minima at certain critical densities. Individually, the Mott (Anderson) MIT has a single critical density whose minimum entanglement decreases as the interaction (disorder) enhances. While in the Mott MIT entanglement saturates at finite values, characterizing partial localization, in the Anderson MIT the system reaches full localization, with zero entanglement, for sufficiently strong disorder. In the combined Mott-Anderson MIT, we find three critical densities referring to local minima on entanglement. One of them is the same as for the Anderson MIT, but now the presence of interaction requires a stronger disorder potential to induce full localization. A second critical density is related to the Mott MIT, but due to disorder it is displaced by a factor proportional to the concentration of impurities. The third local minimum on entanglement is unique to the concomitant presence of disorder and interaction, found to be related to an effective density phenomenon, thus referred to as a Mott-like MIT. Since entanglement has been intrinsically connected to the magnetic susceptibility---a quantity promptly available in cold-atom experiments---our detailed numerical description might be useful for the experimental investigation of the Mott-Anderson MIT.

Sindhunil Barman Roy

Akihisa Koga, Norio Kawakami, Robert Peters +1 more

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.