Spin supersolid in an anisotropic spin-one heisenberg chain

We consider an S = 1 Heisenberg chain with strong exchange (Delta = J(z)/J(perpendicular to)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S = 1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta - B quantum phase diagram using a quantum Monte Carlo method.