Bose liquid in checkerboard antiferromagnet

The frustrated J₁-J₂ antiferromagnet model on the checkerboard lattice, known as the two-dimensional analog of the pyrochlore lattice, provides a perfect platform for dimensional crossover effect due to competition between the two exchange constants J₁ and J₂. Using recently developed tensor network algorithm based on Projected Entangled Simplex States (PESS), we obtain a line degenerate bose liquid state without magnetic order on the whole range of J₂ > J₁ for both XY and Heisenberg antiferromagnetic limit. The degenerate liquid state is stable even when small anisotropy on J₁ bond is introduced and the interaction enhance the robustness of the bose liquid behavior.