Fracton fusion and statistics

Pai, Shriya; Hermele, Michael

doi:10.1103/physrevb.100.195136

Fracton fusion and statistics

Journal Article · Fri Nov 22 00:00:00 EST 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.195136· OSTI ID:1671771

Pai, Shriya ^[1]; ^[2]

Univ. of Colorado, Boulder, CO (United States); University of Colorado Boulder
Univ. of Colorado, Boulder, CO (United States)

We introduce and develop a theory of fusion and statistical processes of gapped excitations in Abelian fracton phases. The key idea is to incorporate lattice translation symmetry via its action on superselection sectors, which results in a fusion theory endowed with information about the nontrivial mobility of fractons and subdimensional excitations. This results in a description of statistical processes in terms of local moves determined by the fusion theory. Our results can be understood as providing a characterization of translation-invariant fracton phases. We obtain simple descriptions of the fusion theory in the X-cube and checkerboard fracton models, as well as for gapped electric and magnetic excitations of some gapless U(1) tensor gauge theories. An alternate route to the X-cube model fusion theory is provided by starting with a system of decoupled two-dimensional toric code layers, and giving a description of the p-string condensation mechanism within our approach. We discuss examples of statistical processes of fractons and subdimensional excitations in the X-cube and checkerboard models. As an application of the ideas developed, we prove that the X-cube and semionic X-cube models realize distinct translation-invariant fracton phases, even when the translation symmetry is broken corresponding to an arbitrary but finite enlargement of the crystalline unit cell.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0014415

OSTI ID:: 1671771

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 19 Vol. 100; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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