Superfluid-insulator transitions on the triangular lattice

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)×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.