We report on a phenomenological study of superfluid to Mott insulator transitions of bosons on the triangular lattice, focusing primarily on the interplay between Mott localization and geometrical charge frustration at
1∕2-filling. A general dual-vortex field theory is developed for arbitrary rational filling factors
f, based on the appropriate projective symmetry group. At the simple nonfrustrated density
f=1∕3, we uncover an example of a deconfined quantum critical point very similar to that found on the half-filled square lattice. Turning to
f=1∕2, the behavior is quite different. Here, we find that the low-energy action describing the Mott transition has an emergent non-Abelian $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry, which is not present at the microscopic level. This large non-Abelian symmetry is directly related to the frustration-induced quasidegeneracy between many charge-ordered states not related by microscopic symmetries. Through this ``pseudospin''
SU(2) symmetry, the charged excitations in the insulator close to the Mott transition develop a Skyrmion-like character. This leads to an understanding of the supersolid phase of the triangular lattice
XXZ model as a ``partially melted'' Mott insulator, for more information see Melko et al. [Phys. Rev. Lett. 95, 127207 (2005)], Heidarian and Damle [Phys. Rev. Lett. 95, 127206 (2005)], and Wessel and Troyer [Phys. Rev. Lett. 95, 127205 (2005)]. The latter picture naturally explains a number of puzzling numerical observations of the properties of this supersolid. Moreover, we predict that the nearby quantum phase transition from this supersolid to the Mott insulator is in the noncompact
CP1 critical universality class as presented in Motrunich and Vishwanath [Phys. Rev. B. 70, 075104 (2004)]. A description of a broad range of other Mott and supersolid states, and a diverse set of quantum critical points between them, is also provided.
The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies (
V) and on-site interspecies (
U) repulsions. For the case of symmetric hopping amplitude (
tA/V=tB/V) and
U/V=1, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, and the latter even survives up to the ${t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ or ${t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The effects induced by the variation of
U/V and by the imbalance of particle numbers of the two species are also explored.
Hard-core bosons on a triangular lattice with nearest-neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order.
We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) 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 approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.