Evidence of a spin liquid with hard-core bosons in a square lattice

We show that laser-assisted hopping of hard-core bosons in a square optical lattice can be described by an antiferromagnetic J(1)-J(2) XY model with a tunable ratio of J(2)/J(1). We numerically investigated the phase diagram of the J(1)-J(2) XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and found strong evidence that in the intermediate region around J(2)/J(1) similar to 0.5, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the J(2) << J(1) side and the stripe antiferromagnetic phase on the J(2) >> J(1) side. This finding opens up the possibility of studying the exotic spin liquid phase in a realistic experimental system using ultracold atoms in an optical lattice.