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Field Theories for type-II fractons

2022; SciPost.org; Volume: 12; Issue: 2 Linguagem: Inglês

10.21468/scipostphys.12.2.064

2542-4653

Weslei Fontana, Pedro R. S. Gomes, Claudio Chamon,

Advanced Condensed Matter Physics

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.