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

TL;DR

This paper demonstrates that hard-core bosons in a square optical lattice can realize an antiferromagnetic J1-J2 XY model, revealing a spin liquid phase around J2/J1 ~ 0.5 through numerical simulations, which could be experimentally observed with ultracold atoms.

Contribution

It provides the first numerical evidence of a spin liquid phase in a J1-J2 XY model realized with hard-core bosons in an optical lattice.

Findings

Identification of a spin liquid phase near J2/J1 ~ 0.5

Evidence of vanishing magnetization and valence bond order in the spin liquid

Connection between Neel and stripe antiferromagnetic phases

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 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.