1104.0721 (Michael J. Lawler)
Michael J. Lawler
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 assuming they are constrained to their lowest energy configurations. 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 suggests that the ground state of Herbertsmithite is insensitive to its out-of-plane impurity moments[1] or Dzyaloshinskii-Moriya interactions
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http://arxiv.org/abs/1104.0721
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