Numerical Investigation of the J₁-J_χ Model on the Heavy-Hexagonal Lattice

Quantum spin liquids are expected to emerge in materials where strong correlations and geometric frustration prevent conventional magnetic ordering. Motivated by recent theoretical and experimental work on the Heavy-Hexagon (HH) lattice formed by Honeycomb-Kagome bilayers, we study an effective spin-1/2 model describing electrons in a magnetic field, subject to infinite onsite Hubbard repulsion. Here, honeycomb and Kagome sites are coupled by spin exchange J₁, and Kagome triangles are coupled by a three-spin chiral interaction J_χ. Using a combination of infinite density matrix renormalization group on cylinders and exact diagonalization on small tori, we study the ground-state phase diagram of this model as a function of J₁/J_χ. For small J₁/J_χ, the kagome spins realize a chiral spin liquid, consistent with previous studies of the kagome-only model. For large J₁/J_χ, the system realizes a SU(2)-symmetric ferrimagnet, arising from the imbalance between sublattices in the HH lattice. At intermediate J₁/J_χ, we discuss the nature of the phase transition out of the chiral spin liquid. Our work highlights honeycomb-Kagome bilayers as an exciting platform for studying strongly correlated and unconventional magnetism.