Field Theories for typeII fractons
Abstract
We derive an effective field theory for a typeII 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 typeI 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 ChernSimonslike 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.
 Publication:

SciPost Physics
 Pub Date:
 February 2022
 DOI:
 10.21468/SciPostPhys.12.2.064
 arXiv:
 arXiv:2103.02713
 Bibcode:
 2022ScPP...12...64F
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 29 pages, 3 figures