Odd fracton theories, proximate orders, and parton constructions
Abstract
The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy nontrivial conditions on their low-energy properties when a combination of lattice translation and U(1) symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other subdimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that “odd” versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd Z2 gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry breaking, thereby allowing us to identify a class of conventionally ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. In conclusion, condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.
- Authors:
-
[1];
[2];
- Univ. of Colorado, Boulder, CO (United States)
- Clarendon Lab., Oxford (United Kingdom)
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); European Research Council (ERC)
- OSTI Identifier:
- 1762129
- Grant/Contract Number:
- SC0014415; 804213-TMCS
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 20; 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; Fractionalization; Gauge theories; Symmetry protected topological states; Topological phases of matter
Citation Formats
Pretko, Michael, Parameswaran, S. A., and Hermele, Michael. Odd fracton theories, proximate orders, and parton constructions. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.205106.
Pretko, Michael, Parameswaran, S. A., & Hermele, Michael. Odd fracton theories, proximate orders, and parton constructions. United States. https://doi.org/10.1103/physrevb.102.205106
Pretko, Michael, Parameswaran, S. A., and Hermele, Michael. Fri .
"Odd fracton theories, proximate orders, and parton constructions". United States. https://doi.org/10.1103/physrevb.102.205106. https://www.osti.gov/servlets/purl/1762129.
@article{osti_1762129,
title = {Odd fracton theories, proximate orders, and parton constructions},
author = {Pretko, Michael and Parameswaran, S. A. and Hermele, Michael},
abstractNote = {The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy nontrivial conditions on their low-energy properties when a combination of lattice translation and U(1) symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other subdimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that “odd” versions of X-cube fracton order can occur in systems at half-odd-integer filling, generalizing the notion of odd Z2 gauge theory to the fracton setting. At half-odd-integer filling, exiting the X-cube phase by condensing fractional quasiparticles leads to symmetry breaking, thereby allowing us to identify a class of conventionally ordered phases proximate to phases with fracton order. We leverage a dual description of one of these ordered phases to show that its topological defects naturally have restricted mobility. In conclusion, condensing pairs of these defects then leads to a fracton phase, whose excitations inherit these mobility restrictions.},
doi = {10.1103/physrevb.102.205106},
journal = {Physical Review. B},
number = 20,
volume = 102,
place = {United States},
year = {Fri Nov 06 00:00:00 EST 2020},
month = {Fri Nov 06 00:00:00 EST 2020}
}
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