Global phase diagram for the spin-1 antiferromagnet with uniaxial anisotropy on the kagome lattice

The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the z-component nearest-neighbor spin interaction J(z) is antiferromagnetic. Besides J(z) and the nearest-neighbor in-plane spin interaction J(xy), the system is also parametrized by an on-site anisotropic term D(S-z)(2). In the zero magnetic field case, the six previously introduced phases, found using various methods, are the nondegenerate gapped photon phase, which breaks no space symmetry or spin symmetry; the sixfold degenerate phase with plaquette order, which breaks both time-reversal symmetry and translational symmetry; the "superfluid" (ferromagnetic) phase with an in-plane global U(1) symmetry broken when J(xy)< 0; the root 3 x root 3 order when J(xy)>0; the nematic phase when D < 0 and large; and a phase with resonating dimers on each hexagon. We obtain all of these phases and partial information about their quantum phase transitions in a single framework by studying condensation of defects in the sixfold plaquette phases. The transition between nematic phase and the sixfold degenerate plaquette phase is potentially an unconventional second-order critical point. In the case of a nonzero magnetic field along z, another ordered phase with translation symmetry broken is opened up in the nematic phase. Due to the breaking of time-reversal symmetry by the field, a supersolid phase emerges between the sixfold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, organic compound m-MPYNN center dot BF4, or optical lattices of atoms with three degenerate states on every site.