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• W4288441796 abstract "We investigate how symmetry and topological order are coupled in the ${2+1}$d $mathbb{Z}_{N}$ rank-2 toric code for general $N$, which is an exactly solvable point in the Higgs phase of a symmetric rank-2 $U(1)$ gauge theory. The symmetry enriched topological order present has a non-trivial realization of square-lattice translation (and rotation/reflection) symmetry, where anyons on different lattice sites have different types and belong to different superselection sectors. We call such particles position-dependent excitations. As a result, in the rank-2 toric code anyons can hop by one lattice site in some directions while only by $N$ lattice sites in others, reminiscent of fracton topological order in ${3+1}$d. We find that while there are $N^2$ flavors of $e$ charges and $2N$ flavors of $m$ fluxes, there are not $N^{N^{2} + 2N}$ anyon types. Instead, there are $N^{6}$ anyon types, and we can use Chern-Simons theory with six $U(1)$ gauge fields to describe all of them. While the lattice translations permute anyon types, we find that such permutations cannot be expressed as transformations on the six $U(1)$ gauge fields. Thus the realization of translation symmetry in the $U^6(1)$ Chern-Simons theory is not known. Despite this, we find a way to calculate the translation-dependent properties of the theory. In particular, we find that the ground state degeneracy on an ${L_{x}times L_{y}}$ torus is ${N^{3}gcd(L_{x},N) gcd(L_{y},N) gcd(L_{x},L_{y},N)}$, where $gcd$ stands for greatest common divisor. We argue that this is a manifestation of UV/IR mixing which arises from the interplay between lattice symmetries and topological order." @default.
• W4288441796 created "2022-07-29" @default.
• W4288441796 creator A5072166156 @default.
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• W4288441796 date "2022-07-28" @default.
• W4288441796 modified "2023-10-14" @default.
• W4288441796 title "Position-dependent excitations and UV/IR mixing in the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi mathvariant=double-struck>Z</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:math> rank-2 toric code and its low-energy effective field theory" @default.
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• W4288441796 doi "https://doi.org/10.1103/physrevb.106.045145" @default.
• W4288441796 hasPublicationYear "2022" @default.
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