Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2011-04-05
Physics
Condensed Matter
Strongly Correlated Electrons
14 pages, 4 figures
Scientific paper
Condensed matter exhibit a wide variety of exotic emergent phenomena, such as the topological order in the fractional quantum Hall effect[1], and the "cooperative paramagnetic" response of geometrically frustrated magnets[2]. Spins exploring the large configuration subspace associated with the latter[3,4] are dominated by collective behavior. Though spins in this emergent regime have been studied numerically[5-7] and analytically through an effective theory[7], their classical and quantum dynamics are not well understood. I consider the constrained classical Hamiltonian dynamics of spins exploring such a configuration space. The method I apply, introduced by Dirac[8-11], suggests that all frustrated magnets have gauge dynamics at least at the semi-classical level. Remarkably, in the kagome lattice model I consider as an example, these dynamics are similar to the "topological" (Chern-Simons) gauge dynamics of electrons in the fractional quantum Hall effect and have non-locally entangled edge modes as the only low energy degrees of freedom. This topological dynamics, which may be found in any nearest neighbor exchange dominated kagome-like antiferromagnet, provides a natural explanation for the apparent insensitivity of the ground state of Herbertsmithite[12] to the out-of-plane impurity moments[13].
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