Unconventional $\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$ topological order in the kagome XY toric code

Abstract:We investigate the quantum phase diagram of the XY toric code (XYTC) on the kagome lattice consisting of $XY$ hexagonal and triangular plaquette operators and conserved star operators. We demonstrate analytically by exploiting an exact local $\mathbb{Z}_2$-symmetry on dodecagons that the kagome XYTC realizes a $\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$ topologically ordered phase in the limit of large hexagonal \mbox{plaquette} operators. This unconventional topological phase involves 64 quasi-particles - Abelian anyons - with restricted mobility on three colored sublattices establishing a quantum dimension of eight. The large number of topological superselection sectors originates from six independent Wilson loop operators, acting as emergent one-form symmetries. The resulting anyon structure is richer than that of established topological codes like the toric and the color code. A corresponding CSS topological stabilizer code is formulated, opening novel possibilities for the encoding and manipulation of topological quantum information.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2607.22296 [cond-mat.str-el]

(or arXiv:2607.22296v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2607.22296 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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