2011

The emergence of gauge invariance: the stay-at-home gauge versus local-global duality

Zaanen, J., Beekman, A. J.

Understand

In condensed matter physics gauge symmetries other than the U(1) of electromagnetism are of an emergent nature.

Two emergence mechanisms for gauge symmetry are well established: the way these arise in Kramers-Wannier type local-global dualities, and as a way to encode local constraints encountered in (doped) Mott insulators.
We demonstrate that these gauge structures are closely related, and appear as counterparts in either the canonical or field-theoretical language.
The restoration of symmetry in a disorder phase transition is due to having the original local variables subjected to a coherent superposition of all possible topological defect configurations, with the effect that correlation functions are no longer well-defined.

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