Superposition, Fragmentation and Spin Liquid in Classical Spins

Abstract

Quantum properties, like superposition, entanglement, and fractionalization, enable fascinating functionalities for quantum technologies. However, it remains unclear whether these properties are exclusive to quantum concepts or can be generalized to the classical vector space. This talk addresses this question. We introduce a generic symmetry group construction built from a vector field in a plaquette of classical spins, demonstrating how classical spins superpose in the irreducible representations (irreps). The corresponding probability amplitudes serve as order parameters and local spins as fragmented excitations. Moreover, the formalism offers a many-body vector field representation for diverse ground states, encompassing spin liquids and fragmented phases described as degenerate ensembles of irreps. Finally, we apply the theory in a square Kagome lattice, showing how the spin liquid state is unstable to either vortex orderings or fragmented phases with any finite Dzyaloshinskii-Mor...