Mott localization nurtures several competing and coexisting orders

Band insulating diamond or metallic mercury differs in a fundamental fashion from materials containing Mott localized electrons. Proliferation of long range orders that compete and sometimes coexist is an important consequence of Mott localization. In this article we focus on how Mott localization creates a rich phase diagram and new physics. A projected nature of the low energy Hilbert space, as opposed to a Fermi gas like Hilbert space, underlies this. Spin, orbital and charge degree of freedom gain independence, but get quantum entangled among themselves and create novel phases. We focus on spin-half single orbital systems. Mott localization encourages entanglement of spin pairs via valence bond formation. We relate valence bond dynamics to emergent gauge fields. Emergent gauge fields in turn nurture and encourage a variety of orders, including topological orders: antiferromagnetism, spin liquids, charge, spin stripes, chiral order and robust superconducting order.     

Correlated electrons in the presence of disorder

Several new aspects of the subtle interplay between electronic correlations and disorder are reviewed. First, the dynamical mean-field theory (DMFT) together with the geometrically averaged (“typical”) local density of states is employed to compute the ground state phase diagram of the Anderson-Hubbard model at half-filling. This non-perturbative approach is sensitive to Anderson localization on the one-particle level and hence can detect correlated metallic, Mott insulating and Anderson insulating phases and can also describe the competition between Anderson localization and antiferromagnetism. Second, we investigate the effect of binary alloy disorder on ferromagnetism in materials with f-electrons described by the periodic Anderson model. A drastic enhancement of the Curie temperature T_c caused by an increase of the local f-moments in the presence of disordered conduction electrons is discovered and explained.     

Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.     

Phase coherence of an atomic Mott insulator

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.     

Quantum magnetism with multicomponent dipolar molecules in an optical lattice

We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/R(3) interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with an ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.     

Quantum insulating states of F=2 cold atoms in optical lattices

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an octopole coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin-ordered insulating phases are ferromagnetic, cyclic, and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.     

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. Received 5 July 2000 and Received in final form 8 November 2000     

On the pressure-temperature phase diagram of intermediate valence compounds

The pressure-temperature (P, T) phase diagram of intermediate valence compounds has been calculated on the basis of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. It is shown that the positive slope (dP/dT>0) of the phase boundary between the insulating and the mixed valence phase as observed experimentally in Sm S and many other systems is determined by the behaviour of the electronic density of states of the interacting system as function ofP. Moreover, the observed anomalous thermal contraction in the insulating phase near the phase boundary and the anomalously large thermal expansion in the metallic phase are well described by numerical results for the extended periodic Anderson model.     

Mott domains of bosons confined on optical lattices

In the absence of a confining potential, the boson-Hubbard model exhibits a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong coupling. We use quantum Monte Carlo simulations to study the ground state of the one-dimensional bosonic Hubbard model in a trap. Some, but not all, aspects of the Mott insulating phase persist. Mott behavior occurs for a continuous range of incommensurate fillings, very different from the unconfined case, and the establishment of the Mott phase does not proceed via a traditional quantum phase transition. These results have important implications for interpreting experiments on ultracold atoms on optical lattices.     

Kondo breakdown as a selective Mott transition in the Anderson lattice

We show within the slave-boson technique that the Anderson lattice model exhibits a Kondo breakdown quantum critical point where the hybridization goes to zero at zero temperature. At this fixed point, the f electrons experience as well a selective Mott transition separating a local-moment phase from a Kondo-screened phase. The presence of a multiscale quantum critical point in the Anderson lattice in the absence of magnetism is discussed in the context of heavy fermion compounds. This study is the first evidence for a selective Mott transition in the Anderson lattice.     

Imaging phase separation near the Mott boundary of the correlated organic superconductors kappa-(BEDT-TTF)2X

Electronic phase separation consisting of the metallic and insulating domains with 50-100 microm in diameter is found in the organic Mott system kappa-[(h8-BEDT-TTF)(1-x)(d8-BEDT-TTF)x]2Cu[N(CN)2]Br by means of scanning microregion infrared spectroscopy using the synchrotron radiation. The phase separation appears below the critical end temperature 35-40 K of the first-order Mott transition. The observation of the macroscopic size of the domains indicates a different class of the intrinsic electronic inhomogeneity from the nanoscale one reported in the inorganic Mott systems such as high-Tc copper and manganese oxides.     

Mott physics near the insulator-to-metal transition in NdNiO3

An optical study of NdNiO(3) ultrathin films with insulating and metallic ground states reveals new aspects of the insulator-to-metal transition that point to Mott physics as the driving force. In contrast with the behavior of charge-ordered systems, we find that the emergence of the Drude resonance across the transition is linked to a spectral weight transfer over an energy range of the order of the Coulomb repulsion U, as the energy gap is filled with states instead of closing continuously.     

Topological Mott insulators

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.     

Numerical finite size scaling approach to many-body localization

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte Carlo simulations while the localization properties are extracted from the "Thouless conductance" g, i.e., the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two-dimensional system of size L. We recover the well-known universal beta(g)=dlogg/dlogL one parameter scaling function without interaction. Upon switching on the interaction, we find that beta(g) is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.     

Phase diagram of electron-hole systems: Interplay between exciton Mott transition and quantum pair condensation

Quasi-thermal-equilibrium states of electron-hole (e-h) systems in photoexcited insulators are studied from a theoretical viewpoint, stressing the exciton Bose-Einstein condensation (BEC), the e-h BCS-type pair-condensed state, and the exciton Mott transition between an insulating exciton/biexciton gas phase and a metallic e-h plasma phase. We determine the quasi-equilibrium phase diagram of the e-h system at zero and finite temperatures with applying the dynamical mean-field theory (DMFT) to the e-h Hubbard model with both repulsive and attractive on-site interactions. Effects of inter-site interactions on the exciton Mott transition are also clarified with applying the extended DMFT to the extended e-h Hubbard model.     

Mechanism of hopping transport in disordered mott insulators

By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca2-xSrxRuO4 near the metal-insulator transition. The hopping exponent alpha shows a systematic evolution from a value of alpha=1/2 deeper in the insulator to the conventional Mott value alpha=1/3 closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induced localized electronic states populating the Mott-Hubbard gap.     

The insulating state of matter: a geometrical theory

In 1964 Kohn published the milestone paper “Theory of the insulating state”, according to which insulators and metals differ in their ground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators.