Phase coherence, visibility, and the superfluid-Mott-insulator transition on one-dimensional optical lattices

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et al. [Phys. Rev. Lett. 95, 050404 (2005); 10.1103/PhysRevLett.95.050404cond-mat/0507087]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that, as the interaction strength U is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than 1.     

Insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group, we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from runaway flows, it allows a direct study of the insulating phases, not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the on-site chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always described by Kosterlitz-Thouless-like flows.     

Janus-faced influence of Hund's rule coupling in strongly correlated materials

We show that in multiband metals the correlations are strongly affected by Hund's rule coupling, which depending on the filling promotes metallic, insulating or bad-metallic behavior. The quasiparticle coherence and the proximity to a Mott insulator are influenced distinctly and, away from single- and half-filling, in opposite ways. A strongly correlated bad metal far from a Mott phase is found there. We propose a concise classification of 3d and 4d transition-metal oxides within which the ubiquitous occurrence of strong correlations in Ru- and Cr-based oxides, as well as the recently measured high Néel temperatures in Tc-based perovskites are naturally explained.     

Competition between crystal field splitting and Hund’s rule coupling in two-orbital magnetic metal-insulator transitions

Competition between crystal field splitting and Hund’s rule coupling in magnetic metal-insulator transitions of half-filled two-orbital Hubbard model is investigated by multi-orbital slave-boson mean field theory. We show that with the increase of Coulomb interaction, the system firstly transits from a paramagnetic (PM) metal to a Néel antiferromagnetic (AFM) Mott insulator, or to a nonmagnetic orbital insulator, depending on the competition of crystal field splitting and the Hund’s rule coupling. The AFM Mott insulating, PM metallic and orbital insulating phases are not, partially and fully orbital polarized, respectively. For a small J _H and a finite crystal field, the orbital insulator is robust. These results demonstrate that large crystal field splitting favors the formation of the orbital insulating phase, while large Hund’s rule coupling tends to destroy it, driving the low-spin to high-spin transition.     

Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.     

Transition from a strongly interacting 1d superfluid to a Mott insulator

We study 1D trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of strong interactions. In the Mott insulating phase a discrete spectrum is measured. Both phases are compared to the 3D situation and to the crossover regime from 1D to 3D. The coherence length and coherent fraction of the gas are measured in all configurations. We observe signatures for increased fluctuations characteristic for 1D systems. Moreover, the collective oscillations cease near the transition to the Mott insulator phase.     

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.     

Can correlations drive a band insulator metallic?

We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.     

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.     

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.     

Cluster dynamical mean field theory of the Mott transition

We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.     

Correlated insulated phase suggests bond order between band and mott insulators in two dimensions

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U > Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.     

Symmetry of the superconducting order parameter in frustrated systems determined by the spatial anisotropy of spin correlations

We study the resonating valence bond theory of the Hubbard-Heisenberg model on the half-filled anisotropic triangular lattice. Varying the frustration changes the wave vector of maximum spin correlation in the Mott insulating phase. This, in turn, changes the symmetry of the superconducting state that occurs at the boundary of the Mott insulating phase. We propose that this physics is realized in several families of quasi-two-dimensional organic superconductors.     

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.     

Subpicosecond time-resolved Mott transition in CuCl

The Mott transition in CuCl from a metallic phase of free electrons and holes towards an insulating phase of bound particles (excitons or biexcitons) has been studied by time-resolved luminescence with a resolution slightly better than 1 ps. The phase change takes place in a very short but finite time (about 3 ps) at a carrier density N 10¹⁹ cm^-3.     

Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

We report the results of the Knight shift by ?3,??Cu-NMR measurements on single-layered copper-oxide Bi?Sr(?-x)La(x)CuO(?+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ?3Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.     

Quantum glass phases in the disordered Bose-Hubbard model

The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.     

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.     

Mott insulators without symmetry breaking

We present theoretical models, in one and two space dimensions, that exhibit Mott insulating ground states at fractional occupations without any symmetry breaking. The Hamiltonians of these models are nonlocal in configuration space, but local in phase space.