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• W2980491973 abstract "Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three dimensions. The key element of this construction is a generalization of higher-form gauge theories to so-called $mathfrak{F}_p$ gauge theories, in which gauge transformations of rank-$k$ fields are specified by rank-$(k - p)$ gauge parameters. The $mathbb{Z}_2$ rank-two theory of type $mathfrak{F}_2$, placed on a cubic lattice and coupled to scalar matter, is shown to have a topological phase exactly dual to the well-known X-cube model. Generalizations of this example yield novel fracton theories. In the continuum, the $mathrm{U}(1)$ rank-two theory of type $mathfrak{F}_2$ is shown to have a perturbatively gapless fracton regime that cannot be consistently interpreted as a tensor gauge theory of any kind. The compact scalar fields that naturally couple to this $mathfrak{F}_2$ theory also show gapless fracton behavior; on a cubic lattice they have a conserved $mathrm{U}(1)$ charge and dipole moment, but these particular charges are not necessarily conserved on more general lattices. The construction straightforwardly generalizes to $mathfrak{F}_2$ theories of nonabelian rank-two gauge fields, giving first examples of pure nonabelian higher-rank theories." @default.
• W2980491973 created "2019-10-25" @default.
• W2980491973 creator A5070884352 @default.
• W2980491973 date "2020-03-10" @default.
• W2980491973 modified "2023-09-27" @default.
• W2980491973 title "Systematic Constructions of Fracton Theories" @default.
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