Evidence of 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 tunable ratio of $J_{2}/J_{1}$. We numerically investigate 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 find strong evidence that in the intermediate region around $% J_{2}/J_{1}\sim 0.5$, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the $J_{2}\ll J_{1}$ side and the stripe antiferromagnetic phase on the $% J_{2}\gg J_{1}$ 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.