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 J1–J2XY model with a tunable ratio of J2/J1. We numerically investigated the phase diagram of the J1–J2XY 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 J2/J1 ∼ 0.5, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Néel state on the J2 ≪ J1 side and the stripe antiferromagnetic phase on the J2 ≫ J1 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.