Figure 4: Phase diagram of spinor bosons in the spin-dependent hexagonal lattice.
From: Chiral magnetism and spontaneous spin Hall effect of interacting Bose superfluids
(a) The phase diagram parameterized by intra- and inter- spin interactions U and V respectively (see Methods). The total density ρ↑+ρ↓ is fixed to be 1 here. In the weakly interacting limit, the chiral spin (χs) superfluid (SF) has a first-order transition to the fully polarized (FP) superfluid state. A partially polarized (PP) SF state is stabilized for intermediate interactions. This PP SF state is also chiral, namely the two spin components condense in opposite valleys (±K). An FP Mott state appears for stronger interactions. The phase boundaries between these polarized states meet at a quantum tricritical point. (b) The polarization as a function of V for different values of U. (c) Tunability of U/V for 87Rb atoms loaded in the spin-dependent hexagonal lattice, as in the experiment11. The lattice depth is chosen to be 0=2Erec, where Erec is the single photon recoil energy.
