We outline a general mechanism for orbital-selective Mott transition, the coexistence of both itinerant and localized conduction electrons, and show how it can take place in a wide range of realistic situations, even for bands of identical width and correlation, provided a crystal field splits the energy levels in manifolds with different degeneracies and the exchange coupling is large enough to reduce orbital fluctuations. The mechanism relies on the different kinetic energy in manifolds with different degeneracy. This phase has Curie-Weiss susceptibility and non-Fermi-liquid behavior, which disappear at a critical doping, all of which is reminiscent of the physics of the pnictides.

We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.

The persistent proximity of insulating and metallic phases, a puzzling characterestic of manganites, is argued to arise from the self organization of the twofold degenerate eg orbitals of M n into localized Jahn-Teller(JT) polaronic levels and broad band states due to the large electron -JT phonon coupling present in them. We describe a new two band model with strong correlations and a dynamical mean-field theory calculation of equilibrium and transport properties. These explain the insulator metal transition and colossal magnetoresistance quantitatively, as well as other consequences of two state coexistence. ∼ 0.5) into a metal in a relatively small(5-7 T esla) magnetic field all suggest that metallic and insulating phases are always very close in free energy. This is also reflected in the ubiquitous coexistence (static or dynamic) of two 'phases', one insulating with local lattice distortion and the other metallic without lattice distortion, with length scales varying from 10A• to 10These phenomena are due to the dynamics of the e g electrons of M n constrained by three strong on-site interactions, namely electron lattice or Jahn-Teller (JT) coupling which splits the twofold e g orbital degeneracy, ferromagnetic e g spin-t 2g spin exchange or Hund's coupling J H and e g electron repulsion U . The respective energies are E JT ≃ 0.5 eV , J H ≃ 2 eV and U ≃ 5 eV , compared to the e g electron intersite hopping t ≃ 0.2 eV which sets the kinetic energy scale [4]. Understanding their observed consequences is one of the major challenges in the physics of strongly interacting electrons. Earlier theoretical attempts neglect one or more of these strong interactions and make further approximations; the predictions do not agree with many characteristics of manganites. For example the ferromagnetic Curie transition in a number of manganites is from an insulator to a metal, for 0.2 < ∼ x < ∼ 0.5. However, a theory with just Hund's coupling, due to Furukawa [5], finds only a metallic phase, while Millis, Muller and Shraiman [6], who additionally include the electron-JT phonon coupling g but treat the JT distortions as static displacements, obtain a metalmetal transition crossing over to an insulator-insulator transition as g increases.We propose and implement here a new approach which incorporates the crucial effects of all the three interactions and is based on a new idea, namely that of coexisting JT polaronic and broad band e g states, which we believe is the key to manganite physics. The idea and some of its consequences are described and calculations based on a new two band model are then outlined.We first discuss the effect of large JT coupling g on the initially twofold degenerate e g orbitals at each lattice site. There is one superposition (labelled ℓ) which, when singly occupied,leads to a polaronic state with local octahedral symmetry breaking M n − O bond distortion and energy −E JT . Its intersite hopping is reduced (for (E JT /hω 0 ) ≫ 1 where ω 0 is the JT phonon mode frequency) by the exponential Huang-Rhys ...

A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin problem can be solved using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength U is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical U for the Mott transition as a function of a frustrating second-neighbor interaction on lattices relevant for various correlated systems, namely the cobaltites, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In additionto a uniform metallic state, we find a p (3) × p (3) charge density wave in a broad doping regime, including commensurate ones. We find that in the large U limit, intersite Coulomb repulsion V strongly suppresses the single-particle weight of the metallic state.