Emergent gauge dynamics of highly 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.

Updated with some appendices moved to the main body of the paper and some additional improvements. 21 pages, 5 figures

References in corpus (7)

• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
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Cited by in corpus (6)

• Topological Boundary Modes in Isostatic Lattices
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Topology in non-linear mechanical systems
• Spin Ice Thin Film: Surface Ordering, Partial Magnetic Wetting and Emergent Square Ice
• Topology and geometry of spin origami
• Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets