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

Cenke Xu; Joel E. Moore

doi:10.1103/PhysRevB.76.104427

paper

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

arXiv:cond-mat/0701635 · doi:10.1103/PhysRevB.76.104427

Abstract

The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the $J_{z}$ coupling is antiferromagnetic. 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 six-fold 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 $J_{x y} < 0$ ; the $3 \times 3$ order when $J_{x y} > 0$ ; 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 six-fold plaquette phases. The transition between nematic phase and the six-fold 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 six-fold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, BF $_{4}$ salts, or optical lattices of atoms with three degenerate states on every site.

arXiv comment17 pages, 16 figures

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

Abstract

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