Field Theories for type-II fractons

Journal Article · 16 February 2022 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.12.2.064 · OSTI ID:1845612

Fontana, Weslei ^[1]; Gomes, Pedro ^[2]; Chamon, Claudio ^[3]

---

1. Londrina State University, Boston University
2. Londrina State University
3. Boston University

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.

• Research Organization: Boston Univ., MA (United States)
• Sponsoring Organization: Coordination of Superior Level Staff Improvement (CAPES); National Council for Scientific and Technological Development (CNPq); USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: FG02-06ER46316
• OSTI ID: 1845612
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 12; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English