Fracton fusion and statistics
Abstract
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 ofmore »
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1671771
- Grant/Contract Number:
- SC0014415
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 19; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Pai, Shriya, and Hermele, Michael. Fracton fusion and statistics. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.195136.
Pai, Shriya, & Hermele, Michael. Fracton fusion and statistics. United States. https://doi.org/10.1103/physrevb.100.195136
Pai, Shriya, and Hermele, Michael. Fri .
"Fracton fusion and statistics". United States. https://doi.org/10.1103/physrevb.100.195136. https://www.osti.gov/servlets/purl/1671771.
@article{osti_1671771,
title = {Fracton fusion and statistics},
author = {Pai, Shriya and Hermele, Michael},
abstractNote = {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.},
doi = {10.1103/physrevb.100.195136},
journal = {Physical Review. B},
number = 19,
volume = 100,
place = {United States},
year = {Fri Nov 22 00:00:00 EST 2019},
month = {Fri Nov 22 00:00:00 EST 2019}
}
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