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

Abstract

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 ∼ 0.5, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Néel 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.