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Effective Gauge Theories of Spin Systems

M. B. Hastings
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Abstract

A large variety of microscopic gauge theories can be written for antiferromagnetic spin systems, including $U(1), SU(2)$, and $Z_N$. I consider the question of the appropriate effective gauge theory for such systems. I show that while an SU(N) anti-ferromagnet can be written microscopically as a Z_N gauge theory, for unfrustrated systems, with a two-sublattice structure, there is always an effective U(1) gauge field. The dispersion relation for the gauge field is shown to depend on the presence or absence of charge-conjugation symmetry. Frustrated systems can break the gauge group to a discrete group, but this appears to always involve introducing a gap for the spinons.

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M. B. Hastings. 2000-11-09. Effective Gauge Theories of Spin Systems. https://arxiv.org/abs/cond-mat/0011125

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