We study hard-core bosons with unfrustrated hopping (t) and nearest neighbour repulsion (U ) on the triangular lattice. At half-filling, the system undergoes a zero temperature (T ) quantum phase transition from a superfluid phase at small U to a supersolid at Uc ≈ 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic √ 3 × √ 3 pattern, and is remarkably stable-indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t. Introduction: The observation of strongly correlated Mott insulating states and T = 0 superfluid-insulator transitions of ultracold bosonic atoms subjected to optical lattice potentials 1 has led to a great deal of interest in strongly correlated lattice systems that can be realized in such experiments.2,3 The recent observation of a supersolid phase in Helium 4 leads, in this context, to a natural question: Can the lattice analog of this, namely a superfluid phase that simultaneously breaks lattice translation symmetry, be seen in atom-trap experiments?One class of promising candidates are systems which are superfluid when interactions are weak, but form insulators with spatial symmetry breaking when interactions are strong: In terms of conventional Landau theory, a direct transition between these two states is generically either first order, or pre-empted by an intermediate supersolid phase with both order parameters nonzero; both types of behaviour are known to occur in specific lattice models.5,6,7 Moreover, as has been shown recently by Senthil et. al., 8 conventional Landau theory can fail in certain situations in which quantum mechanical Berry phase effects produce a direct second-order phase transition, thereby ruling out an intermediate supersolid phase. When such a transition occurs, 9,10 it is associated with quasi-particle fractionalization and deconfinement, and this alternative to an intermediate supersolid phase is thus interesting in its own right.Bosons on the triangular lattice with on-site repulsion V , repulsive nearest neighbour interaction U , and unfrustrated hopping (t) provide a particularly interesting example in this context since the structure of interactions is simple enough that it can be realized in atom-trap experiments.2,11 In the hard-core V → ∞ limit (which is also experimentally feasible 2,11 ) this maps to a system of S = 1/2 spins (S

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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.

We apply well established finite temperature Quantum Monte Carlo techniques to one dimensional Bose systems with soft and hardcore constraint, as well as to spinless fermion systems. We give clear and robust numerical evidence that, as expected, no superfluid density for Bosons or Meissner fraction for fermions. is possible at any non zero temperature in one dimensional interacting Bose or fermi lattice models, whereas a finite Drude weight is generally observed in gapless systems, in partial disagreement to previous expectations.

We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling J(z) > 0 and unfrustrated (J(perpendicular) < 0) or frustrated (J(perpendicular) >0) kinetic terms in a zero magnetic field. Incorporating long-range Jastrow correlations over a mean-field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary J(z) and either sign of J(perpendicular). For J(perpendicular) < 0, we find a square root(3) x square root(3) supersolid for J(z)/J(perpendicular)| approximately > 4.7, in excellent agreement with quantum Monte Carlo data. For J(perpendicular) > 0, a distinct square root(3) x square root(3) supersolid is found to emerge for J(z)/J(perpendicular) > or = 1. Both supersolids exhibit a spontaneous density deviation from half-filling. At J(z)/J(perpendicular) = infinity, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.

We study local moment formation for adatoms on bilayer graphene (BLG) within a mean field theory of the Anderson impurity model. The wavefunctions of the BLG electrons induce strong particle-hole asymmetry and band dependence of the hybridization, which is shown to result in unusual features in the impurity model phase diagram. We also study the effect of varying the chemical potential, as well as varying an electric field perpendicular to the bilayer; the latter modifies the density of states of electrons in BLG, and, more significantly, shifts the impurity energy. We show that this leads to regimes in the impurity phase diagram where local moments can be turned on or off by applying modest external electric fields. Finally, we show that the RKKY interaction between local moments can be varied by tuning of the chemical potential (as has also been suggested in monolayer graphene) or, more interestingly, by tuning the electric field so that it induces changes in the band structure of BLG.

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