Highly frustrated magnets: a class of emergent gauge systems

Condensed matter exhibit a wide variety of exotic emergent phenomena, such as the topological order in the fractional quantum Hall effect, and the ``cooperative paramagnetic'' response of geometrically frustrated magnets. The classical and quantum dynamics of spins exploring the large configuration space associated with the latter are not well understood analytically. I consider the constrained classical Hamiltonian dynamics of spins exploring such a configuration space as a starting point from which a complete classical and semi-classical description may be reached. The method I employ, introduced by Dirac [1] and now forms the basis of gauge theory, applies to any frustrated system constrained to a continuous set of configurations. Remarkably, in the kagome lattice model I consider as an example, these dynamics are similar to the ``topological'' (Chern-Simons) dynamics of electrons in the fractional quantum Hall effect and have non-locally entangled edge modes as the only degrees of freedom. In principle, these edge states may be found in any kagome-like Heisenberg antiferromagnets such as Herbertsmithite, the Jarosites, SrCr$_{8-x}$G$_{4+x}$O$_{19}$ and Na$_4$Ir$_3$O$_8$. \\[4pt] [1] Dirac, P. A. M. {\it Generalized hamiltonian dynamics}. Can. J. of Math. {\bf 2}, 129-148 (1950)