Alladi Ramakrishnan Hall

The quantum spin quadrumer

Subhankar Khatua

IMSc

Prototypical examples of frustrated magnetism are composed of clusters of $N$ spins with a Hamiltonian proportional to the square of the total spin. The cases with $N=2$ and $3$ are well studied with relevance to square and triangular lattice antiferromagnets. In both cases, several insights have emerged from a large-S, semi-classical field theoretic description. Here, we develop such a theory for $N=4$ clusters. This problem has rich mathematical structure with a ground state space that has non-manifold character, characterized by an $SO(3)$ rotor field and an emergent vector order parameter. We show that, in the low energy limit, the $N=4$ cluster maps to a free spin-$S$ spin and a rigid rotor.
Although this parametrization fails at isolated points, it successfully describes the energy spectrum and its associated degeneracies. We discuss experimental realizations and signatures. Our study paves the way for field theoretic descriptions of systems such as pyrochlore magnets.