Resonating quantum three-coloring wave functions for the kagome quantum antiferromagnet

Motivated by the recent discovery of a macroscopically degenerate exactly solvable point of the spin-1/2XXZ model for Jz/J=-1/2 on the kagome lattice [H. J. Changlani Phys. Rev. Lett. 120, 117202 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.117202] - a result that holds for arbitrary magnetization - we develop an exact mapping between its exact "quantum three-coloring" wave functions and the characteristic localized and topological magnons. This map, involving "resonating two-color loops," is developed to represent exact many-body ground state wave functions for special high magnetizations. Using this map we show that these exact ground state solutions are valid for any Jz/J≥-1/2. This demonstrates the equivalence of the ground-state wave function of the Ising, Heisenberg, and XY regimes all the way to the Jz/J=-1/2 point for these high magnetization sectors. In the hardcore bosonic language, this means that a certain class of exact many-body solutions, previously argued to hold for purely repulsive interactions (Jz≥0), actually hold for attractive interactions as well, up to a critical interaction strength. For the case of zero magnetization, where the ground state is not exactly known, we perform density matrix renormalization group calculations. Based on the calculation of the ground state energy and measurement of order parameters, we provide evidence for a lack of any qualitative change in the ground state on finite clusters in the Ising (Jz J), Heisenberg (Jz=J), and XY (Jz=0) regimes, continuing adiabatically to the vicinity of the macroscopically degenerate Jz/J=-1/2 point. These findings offer a framework for recent results in the literature and also suggest that the Jz/J=-1/2 point is an unconventional quantum critical point whose vicinity may contain the key to resolving the spin-1/2 kagome problem.