Decohering Kitaev's Sixteenfold Way: A Holographic Approach
Abstract
We study anyon decoherence in 2D topological order, with the fermion decoherence in Kitaev's sixteenfold way as explicit examples. The sixteenfold way includes chiral topological phases, which are believed to admit no commuting projector Hamiltonian, making it challenging to study their decoherence directly. We further conjecture the density matrix produced by this decoherence induced phase transition can be obtained by a three-step procedure: first lift the topological order to its Walker-Wang model, followed by a transition to another Walker-Wang model, and finally trace over the bulk degrees of freedom. This establishes a connection between the decoherence of a topological order and a pure state phase transition in its 3D counterpart. Many examples are given. In particular, we show that decohering the fermion in each of the sixteen states always yields an intrinsically mixed-state topological order, a consequence of the fact the corresponding 3D bulk always transits into the 3D fermionic toric code (fTC). Our result suggests a systematic method for studying anyon decoherence in chiral topological orders at the level of commuting projector Hamiltonians.
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BibTeX
@misc{zhang2026decohering,
title = {{Decohering Kitaev's Sixteenfold Way: A Holographic Approach}},
author = {Shuyu Zhang and Linhao Li and Zhen Bi and Tzu-Chieh Wei and Zijian Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03610},
eprint = {2610.03610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03610},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Decohering Kitaev's Sixteenfold Way: A Holographic Approach
AU - Shuyu Zhang
AU - Linhao Li
AU - Zhen Bi
AU - Tzu-Chieh Wei
AU - Zijian Song
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03610
UR - https://arxiv.org/abs/2610.03610
AB - We study anyon decoherence in 2D topological order, with the fermion decoherence in Kitaev's sixteenfold way as explicit examples. The sixteenfold way includes chiral topological phases, which are believed to admit no commuting projector Hamiltonian, making it challenging to study their decoherence directly. We further conjecture the density matrix produced by this decoherence induced phase transition can be obtained by a three-step procedure: first lift the topological order to its Walker-Wang model, followed by a transition to another Walker-Wang model, and finally trace over the bulk degrees of freedom. This establishes a connection between the decoherence of a topological order and a pure state phase transition in its 3D counterpart. Many examples are given. In particular, we show that decohering the fermion in each of the sixteen states always yields an intrinsically mixed-state topological order, a consequence of the fact the corresponding 3D bulk always transits into the 3D fermionic toric code (fTC). Our result suggests a systematic method for studying anyon decoherence in chiral topological orders at the level of commuting projector Hamiltonians.
ER -