2021/03/31 by Weslei B. Fontana, Weslei Fontana, Pedro R. S. Gomes +1
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Constraint (computer-aided design) #Field theory (psychology) #Fracton #Geometry #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Projector #Quantum many-body systems #Theoretical and Computational Physics #Theoretical physics #cond-mat.str-el #hep-th
paper · pdf · doi:10.21468/scipostphys.12.2.064
published as SciPost Phys. 12, 064 (2022) · 29 pages, 3 figures
arxiv created 2022/02/16 · openalex publication_date 2022/02/16 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.