limit*

Exactly solvable Hamiltonians form important cornerstones in our understanding of quantum magnetism. Recently a class of ground state solvable (GSS) frustrated quantum magnets on any lattice composed of triangular motifs has been reported¹. The exact solutions (ES) require consistent three-coloring of the lattice sites. We apply the general principle of exact coloring GSS to long-range magnetic order on the triangular and extend it to unfrustrated bipartite lattices where the ES corresponds to a two-coloring ground state (GS). For several magnetization sectors, we show how the presence of ES in the deep XY regime of the XXZ model accounts for the corresponding antiferromagnetically ordered GS. We numerically demonstrate that for square and triangular lattice, the ordered physics of the solvable points respectively at J_z /J_xy (=Δ)=-1 and Δ=-0.5 adiabatically extend close to the Heisenberg regime Δ∼1. These findings are contrasted with an anisotropic generalization of the Majumdar-Ghosh model, which is proven to have exact dimer GS and three-coloring GS at Δ=-0.5, but where only the former survives as the GS for Δ>-0.5.

1. PRL 120, 117202 (2018); PRB 99, 104433 (2019)