A review of Monte Carlo simulations for the Bose–Hubbard model with diagonal disorder

We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.     

Energy-resolved spatial inhomogeneity of disordered Mott systems

We investigate the effects of weak to moderate disorder on the T=0 Mott metal-insulator transition in two dimensions. Our model calculations demonstrate that the electronic states close to the Fermi energy become more spatially homogeneous in the critical region. Remarkably, the higher energy states show the opposite behavior: they display enhanced spatial inhomogeneity precisely in the close vicinity to the Mott transition. We suggest that such energy-resolved disorder screening is a generic property of disordered Mott systems.     

Universality of liquid-gas Mott transitions at finite temperatures

We explain, in a consistent manner, the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally.     

Phase transition in a system of one-dimensional bosons with strong disorder

We study one-dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach, we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.     

Particle-hole symmetry and the effect of disorder on the Mott-Hubbard insulator

The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( p-h) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when p-h symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when p-h symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is p-h symmetry, whereas in its absence the gap diminishes with increasing disorder.     

Disorder and pseudogap in strongly correlated systems: Phase diagram in the DMFT + Σ approach

The influence of disorder and pseudogap fluctuations on the Mott insulator-metal transition in strongly correlated systems has been studied in the framework of the generalized dynamic mean field theory (DMFT + Σ approach). Using the results of investigations of the density of states (DOS) and optical conductivity, a phase diagram (disorder-Hubbard interaction-temperature) is constructed for the paramagnetic Anderson-Hubbard model, which allows both the effects of strong electron correlations and the influence of strong disorder to be considered. Strong correlations are described using the DMFT, while a strong disorder is described using a generalized self-consistent theory of localization. The DOS and optical conductivity of the paramagnetic Hubbard model have been studied in a pseudogap state caused by antiferromagnetic spin (or charge) short-range order fluctuations with a finite correlation length, which have been modeled by a static Gaussian random field. The effect of a pseudogap on the Mott insulator-metal transition has been studied. It is established that, in both cases, the static Gaussian random field (related to the disorder or pseudogap fluctuations) leads to suppression of the Mott transition, broadening of the coexistence region of the insulator and metal phases, and an increase in the critical temperature at which the coexistence region disappears.     

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.     

Anderson localisation on the Falicov-Kimball model with Coulomb disorder

The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phasediagrams are obtained by means of dynamical mean-field theory applied to the Bethelattice, in which metal-insulator transitions driven by Anderson and Coulomb disorder canbe identified. Metallic, Mott insulator, and Anderson insulator phases, as well as thecrossover between them are studied in this framework. We show that Coulomb disorder has arelevant role in the phase-transition behaviour as the system is led towards the insulatorregime.     

Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions

The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.     

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Creation of a molecular condensate by dynamically melting a Mott insulator

We propose the creation of a molecular Bose-Einstein condensate by loading an atomic condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms per site. Molecules in a Mott insulator state are then created under well defined conditions by photoassociation with essentially unit efficiency. Finally, the Mott insulator is melted and a superfluid state of the molecules is created. We study the dynamics of this process and photoassociation of tightly trapped atoms.     

Stripe glasses: self-generated randomness in a uniformly frustrated system

We show that a system with competing interactions on different length scales, relevant to the formation of stripes in doped Mott insulators, undergoes a self-generated glass transition which is caused by the frustrated nature of the interactions and not related to the presence of quenched disorder. An exponentially large number of metastable configurations is found, leading to a slow, landscape dominated long time relaxation and a breakup of the system into a disordered inhomogeneous state.     

Effect of long range coulomb interactions on the mott transition

We reconsider the Mott transition problem in the presence of long range Coulomb interactions. Using an extended dynamical mean field theory (DMFT) that sums an important class of diagrams absent in ordinary DMFT, we show that in the presence of Coulomb interactions, the zero temperature Mott transition is, as envisioned by Mott, discontinuous in two and three dimensions.     

Dielectric breakdown and avalanches at nonequilibrium metal-insulator transitions

Motivated by recent experiments on the finite temperature Mott transition in VO(2) films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to metal with increasing temperature and voltage at random thresholds due to quenched disorder. We describe the properties of the resulting nonequilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of boltlike avalanches from percolationlike ones.     

Boson Mott insulators at finite temperatures

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where Mott insulator features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression.     

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.     

Inhomogeneous metallic phase in a disordered Mott insulator in two dimensions

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at a disorder V(c1), while antiferromagnetism persists up to a higher V(c2). Most unexpectedly, between V(c1) and V(c2) the system is metallic and is sandwiched between the Mott insulator below V(c1) and the Anderson insulator above V(c2). The metal is formed when the spectral gap gets destroyed locally in regions where the disorder potential is high enough to overcome the interelectron repulsion. This generates puddles with enhanced charge fluctuations that percolate with increasing disorder, resulting in a spatially inhomogeneous metallic phase.     

Doping-driven orbital-selective Mott transition in multi-band Hubbard models with crystal field splitting

We have studied the doping-driven orbital-selective Mott transition in multi-band Hubbard models with equal band width in the presence of crystal field splitting. Crystal field splitting lifts one of the bands while leaving the others degenerate. We use single-site dynamical mean-field theory combined with continuous time quantum Monte Carlo impurity solver to calculate a phase diagram as a function of total electron filling N and crystal field splitting Δ. We find a large region of orbital-selective Mott phase in the phase diagram when the doping is large enough. Further analysis indicates that the large region of orbital-selective Mott phase is driven and stabilized by doping. Such models may account for the orbital-selective Mott transition in some doped realistic strongly correlated materials.     

Phase separation close to the density-driven Mott transition in the Hubbard-Holstein model

The density-driven Mott transition is studied by means of dynamical mean-field theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by a phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling, a polaronic phase emerges coexisting with a nonpolaronic metal.