heisenberg kagome antiferromagnet; quantum hall states; ground-state;field-theory; spin-liquid; order; system; model
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 toward a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and toward a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.
Lawler, M. J. (2013). Emergent gauge dynamics of highly frustrated magnets. New Journal of Physics, 15(4), 043043.
Lawler, Michael J., "Emergent gauge dynamics of highly frustrated magnets" (2013). Physics, Applied Physics and Astronomy Faculty Scholarship. 6.