Energy Landscape and Phase-Space Connectivity of Coplanar Ground States in the Kagome Heisenberg Antiferromagnet

The Kagome lattice, composed of corner-sharing triangles, is a canonical system for studying geometric frustration in quantum magnetism. This work explores the energy landscape of the S = 1/2 Kagome Heisenberg antiferromagnet by analyzing the manifold of coplanar ground states and their connectivity through weathervane rotations. Using a computational framework with periodic boundary conditions, we construct finite Kagome lattices, identify alternating-color loops, and compute magnon spectra via Holstein–Primakoff transformations. All coplanar ground states are found to be degenerate at quadratic order, and the energy barriers between them scale linearly with loop length in the thermodynamic limit. Network and disconnectivity graph analyses reveal a hierarchically organized landscape with highly connected √3×√3 hub states and bottleneck configurations that constrain transitions between basins. Statistical studies of connectivity and loop length distributions uncover Gaussian and power-law behaviors, respectively, indicating that the manifold is both extensive and self-similar. Finally, perturbative analysis explains the Kagome lattice's distinctive linear energy-minimum behavior compared to other frustrated systems. Together, these results present a unified view of the Kagome antiferromagnet's complex energy topology and its link to frustration-induced glassiness.