Lattice Clifford fractons and their Chern-Simons-like theory

Fontana, Weslei Bernardino; Gomes, Pedro R. S.; Chamon, Claudio

doi:10.21468/SciPostPhysCore.4.2.012

SciPost Physics Core

Lattice Clifford fractons and their Chern-Simons-like theory

Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon

SciPost Phys. Core 4, 012 (2021) · published 11 May 2021

doi: 10.21468/SciPostPhysCore.4.2.012
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Abstract

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.4.2.012
TI  - Lattice Clifford fractons and their Chern-Simons-like theory
PY  - 2021/05/11
UR  - https://www.scipost.org/SciPostPhysCore.4.2.012
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 4
IS  - 2
SP  - 012
A1  - Fontana, Weslei Bernardino
AU  - Gomes, Pedro R. S.
AU  - Chamon, Claudio
AB  - We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.
ER  -

@Article{10.21468/SciPostPhysCore.4.2.012,
	title={{Lattice Clifford fractons and their Chern-Simons-like theory}},
	author={Weslei B. Fontana and Pedro R. S. Gomes and Claudio Chamon},
	journal={SciPost Phys. Core},
	volume={4},
	pages={012},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.4.2.012},
	url={https://scipost.org/10.21468/SciPostPhysCore.4.2.012},
}

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Funders for the research work leading to this publication

Boston University [BU]
Conselho Nacional de Desenvolvimento Científico e Tecnológico / National Council for Scientific and Technological Development [CNPq]
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (through Organization: Coordenação de Aperfeicoamento de Pessoal de Nível Superior [CAPES])
United States Department of Energy [DOE]