Energy landscape of the kagome antiferromagnet: Characterization of multiple energy scales

TL;DR

This paper explores the energy landscape of the kagome antiferromagnet, revealing a hierarchy of energy barriers associated with loop sizes that influence its dynamical properties.

Contribution

It characterizes the energy barriers and landscape structure of the kagome antiferromagnet using both exact and statistical methods, highlighting multiple energy scales.

Findings

Dominant low barriers linked to six-spin loops

Broader higher barriers from longer loops

Hierarchy of energy scales influences dynamics

Abstract

We investigate the energy landscape of the kagome Heisenberg antiferromagnet within its coplanar ground-state manifold. Although coplanar states are degenerate at harmonic order, transitions between them require collective weathervane-loop rotations whose barriers grow strongly with loop size. To characterize this structure, we construct disconnectivity graphs using two complementary approaches: exact enumeration and minimax-barrier calculations for small lattices, and a statistical construction for large lattices based on random walks through configuration space, with loop length used as a proxy for barrier height. The exact landscape reveals a dominant low-barrier scale associated with elementary six-spin loops and a broader higher-barrier sector from longer rearrangements. For large systems, the statistical analysis exposes a hierarchy of barrier scales, including a pronounced six-spin-loop peak and an intermediate scale-free regime of loop lengths. This hierarchy provides a natural basis for multiple dynamical time scales: six-spin loops govern the fastest local relaxation, while slower collective dynamics arise from activation of longer loops. These results show that the coplanar manifold is dynamically rugged, with its low-energy dynamics governed by a hierarchy of loop-mediated barriers.