Splitting of the ground state manifold of classical Heisenberg spins as couplings are varied

TL;DR

This paper investigates how the ground state manifold of classical Heisenberg spins can split into many disconnected parts as interaction couplings are varied, providing exact counts in specific lattice constructions.

Contribution

The authors construct spin clusters with tunable interactions where the ground state manifold fragments into multiple disconnected components, including an exact enumeration in one lattice case.

Findings

Ground state manifold can split into exponentially many disconnected pieces.

Explicit construction of spin clusters with controllable ground state topology.

Exact counting of disconnected ground states in a specific lattice.

Abstract

We construct clusters of classical Heisenberg spins with two-spin $\vec{S}_i.\vec{S}_j$-type interactions for which the ground state manifold consists of disconnected pieces. We extend the construction to lattices and couplings for which the ground state manifold splits into an exponentially large number of disconnected pieces at a sharp point as the interaction strengths are varied with respect to each other. In one such lattice we construct, the number of disconnected pieces in the ground state manifold can be counted exactly.