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Based on several previous examples, we summarize explicitly thegeneral procedure to gauge models with subsystem symmetries, which aresymmetries with generators that have support within a sub-manifold ofthe system. The gauging process can be applied to any local quantummodel on a lattice that is invariant under the subsystem symmetry. Wefocus primarily on simple 3D paramagnetic states with planar symmetries.For these systems, the gauged theory may exhibit foliated fracton orderand we find that the species of symmetry charges in the paramagnetdirectly determine the resulting foliated fracton order. Moreover, wefind that gauging linear subsystem symmetries in 2D or 3D models resultsin a self-duality similar to gauging global symmetries in 1D.
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Hydrodynamics of higher-rank gauge theories
We extend recent work on hydrodynamics with global multipolarsymmetries — known as “fracton hydrodynamics” — to systems in which themultipolar symmetries are gauged. We refer to the latter as “fractonmagnetohydrodynamics”, in analogy to conventional magnetohydrodynamics(MHD), which governs systems with gauged charge conservation. We showthat fracton MHD arises naturally from higher-rank Maxwell’s equationsand in systems with one-form symmetries obeying certain constraints;while we focus on “minimal” higher-rank generalizations of MHD thatrealize diffusion, our methods may also be used to identify other, moreexotic hydrodynamic theories (e.g., with magnetic subdiffusion). Incontrast to semi-microscopic derivations of MHD, our approach elucidatesthe origin of the hydrodynamic modes by identifying the correspondinghigher-form symmetries. Being rooted in symmetries, the hydrodynamicmodes may persist even when the semi-microscopic equations no longerprovide an accurate description of the system.
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- Award ID(s):
- 2145544
- PAR ID:
- 10472281
- Publisher / Repository:
- SciPost
- Date Published:
- Journal Name:
- SciPost Physics
- Volume:
- 14
- Issue:
- 3
- ISSN:
- 2542-4653
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhys.14.3.029
