Emergent gauge dynamics of highly frustrated magnets

TL;DR

This paper explores the classical gauge dynamics in highly frustrated magnets, specifically kagome antiferromagnets, revealing topological features and edge states akin to quantum Hall systems, advancing understanding of spin liquid phases.

Contribution

It introduces a classical gauge theory framework for frustrated magnets, linking their dynamics to topological gauge systems like doubled Chern-Simons theory, and provides a semi-classical approach to spin liquids.

Findings

Kagome antiferromagnet exhibits gauge system behavior with topological dynamics.

Edge states in open boundary conditions resemble doubled Chern-Simons electrodynamics.

Classical theory offers a pathway to understanding spin liquid phases in frustrated magnets.

Abstract

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.