Phase-space networks and connectivity of the kagome antiferromagnet

Abstract

We study the coplanar ground-state manifold of the kagome Heisenberg antiferromagnet using a phase-space network representation, in which nodes correspond to coplanar ground states and edges represent transitions generated by weathervane loop rotations. In the coplanar manifold, each configuration can be mapped to a three-coloring problem on the dual honeycomb lattice, where a weathervane mode corresponds to a closed loop of two alternating colors. By comparing networks that include all weathervane loops with networks restricted to elementary six-spin loops, we examine how energetic constraints shape phase-space structure. We find that connectivity distributions are sharply peaked in large systems, while restrictions to short loops reduce typical connectivity. Spectral properties further distinguish the two cases, with short-loop networks exhibiting Gaussian spectra and full networks displaying non-Gaussian features associated with correlated loop updates. Finally, a box-counting analysis reveals distinct fractal properties of the two networks, demonstrating how energetic constraints control the global geometry of configuration space. These results show that the hierarchy of weathervane loop rotations provides a direct link between microscopic constraints and emergent phase-space geometry in a frustrated magnet.

13 pages, 8 figures. v2: matches published version

References in corpus (10)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Scaling theory of fractal complex networks
• Colorings of odd or even chirality on hexagonal lattices
• Multiple time scales from hard local constraints: glassiness without disorder
• Gaussian Networks Generated by Random Walks