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

• URL: http://arxiv.org/abs/2607.22296v1
• Date: Fri, 24 Jul 2026 13:39:45 GMT
• Title: Unconventional $\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$ topological order in the kagome XY toric code
• Abstract summary: 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.<n>We show that the kagome XYTC realizes a $mathbbZologicallytimesmathbbZ$ top ordered phase in the limit of large hexagonal mboxplaquette operators.<n>This unconventional topological phase involves 64 quasi-particles - Abelian anyons - with restricted mobility on three colored sublattices establishing a quantum dimension of eight.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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