Phase-space networks and connectivity of the kagome antiferromagnet

TL;DR

This paper explores the structure of the phase space of the kagome antiferromagnet's ground states using a network model, revealing how energetic constraints influence the connectivity, spectral properties, and fractal geometry of the configuration space.

Contribution

It introduces a phase-space network representation for the kagome antiferromagnet's ground states, linking microscopic loop constraints to the global phase-space structure.

Findings

Connectivity distributions are sharply peaked in large systems.

Restrictions to short loops reduce typical connectivity.

Spectral properties differ between full and restricted networks.

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.