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arXiv · 2103.02713

Field Theories for type-II fractons

Weslei B. Fontana·Pedro R. S. Gomes·Claudio Chamon
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Abstract

We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

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Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon. 2021-03-03. Field Theories for type-II fractons. https://doi.org/10.21468/scipostphys.12.2.064

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