Magnetic Field-induced Spin Supersolid Phases on the Triangular Lattice Heisenberg Antiferromagnets

The supersolid features coexisting superfluidity and spatial symmetry breaking order which is originally proposed as an exotic quantum state in Helium. Given the fact that the boson models can be mapped to the spin models, the spin supersolid may also exist in frustrated spin lattice models with the triangular lattice Heisenberg antiferromagnets as the most promising platform. Motivated by the recent experimental observation of supersolid phases in various triangular lattice compounds, we numerically study the magnetic field induced spin supersolid phases in the spin-1/2 nearest neighbor Heisenberg model with anisotropy. We show consistent results of the off-diagonal order parameters and superfluid stiffness which identify two distinct supersolid phases and the up-up-down phase between them. We also map out the phase diagram with finite magnetic fields that can be compared with experiments. Furthermore, we obtain the spin spectral functions which shows different characteristics for each supersolid phase and the up-up-down phase. In the presence of finite impurities, the spectral functions remain almost the same for the supersolid phases, as opposed to the up-up-down phase where clear differences are found.