Emergent gauge dynamics of highly frustrated magnets

DOI10.1088/1367-2630/15/4/043043zbMATH Open1451.81353arXiv1104.0721OpenAlexW3099377446MaRDI QIDQ5141471

Publication date: 18 December 2020

Published in: New Journal of Physics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1104.0721

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Many-body theory; quantum Hall effect (81V70) Topological field theories in quantum mechanics (81T45)

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