Towards Classification of Fracton Phases: The Multipole Algebra
Abstract
We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of chargedmore »
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1559075
- Alternate Identifier(s):
- OSTI ID: 1630614
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Gromov, Andrey. Towards Classification of Fracton Phases: The Multipole Algebra. United States: N. p., 2019.
Web. doi:10.1103/PhysRevX.9.031035.
Gromov, Andrey. Towards Classification of Fracton Phases: The Multipole Algebra. United States. https://doi.org/10.1103/PhysRevX.9.031035
Gromov, Andrey. Tue .
"Towards Classification of Fracton Phases: The Multipole Algebra". United States. https://doi.org/10.1103/PhysRevX.9.031035.
@article{osti_1559075,
title = {Towards Classification of Fracton Phases: The Multipole Algebra},
author = {Gromov, Andrey},
abstractNote = {We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of charged excitations, fracton phases of both types as well as various Symmetry-protected topological phases emerge. Finally, the relation between the present approach and the formalism based on polynomials over finite fields is discussed.},
doi = {10.1103/PhysRevX.9.031035},
journal = {Physical Review. X},
number = 3,
volume = 9,
place = {United States},
year = {Tue Aug 27 00:00:00 EDT 2019},
month = {Tue Aug 27 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevX.9.031035
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Cited by: 87 works
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Figures / Tables:
FIG. 1: (a) The charge configuration corresponding to qij ∝ σ1. (b) The charge configuration corresponding to qij ∝ σ3. (c) A more convenient basis of charge configurations is obtained by applying (a) and inverse of (a) at plaquettes labeled by star and −1 star correspondingly.
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