Mixed-State Topological Transition and Emergent Fractionalized Supersymmetry in the Non-Abelian Kitaev Spin Liquid
Abstract
We study a mixed-state topological transition in the non-Abelian Kitaev spin liquid driven by a bond-dephasing channel. In the vectorized picture, bond dephasing maps onto interactions between two time-reversed fractionalized Majorana systems coupled to gapped ℤ2 gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting IsingboxtimesIsing̅ to toric-code order in the Choi state and yielding intrinsically mixed-state topological order upon unfolding. More interestingly, at a temporal interface between topological and trivial Kitaev states, a Chern-number mismatch enforces a gapless Majorana mode. Dephasing then drives a mixed-state topological transition at which the gapless mode develops emergent 𝒩=1 supersymmetry. Our Monte Carlo simulations yield ν=1.27(3) and ηb≃ηf≃0.40, consistent with the exact supersymmetric values 5/4 and 2/5. The supersymmetric partners are fractionalized and appear physically as distinct gauge-invariant spin strings, providing concrete observables for future experiments.
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BibTeX
@misc{wan2026mixedstate,
title = {{Mixed-State Topological Transition and Emergent Fractionalized Supersymmetry in the Non-Abelian Kitaev Spin Liquid}},
author = {Zhou-Quan Wan and Hong Yao and Shao-Kai Jian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38741},
eprint = {2610.38741},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38741},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mixed-State Topological Transition and Emergent Fractionalized Supersymmetry in the Non-Abelian Kitaev Spin Liquid
AU - Zhou-Quan Wan
AU - Hong Yao
AU - Shao-Kai Jian
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38741
UR - https://arxiv.org/abs/2610.38741
AB - We study a mixed-state topological transition in the non-Abelian Kitaev spin liquid driven by a bond-dephasing channel. In the vectorized picture, bond dephasing maps onto interactions between two time-reversed fractionalized Majorana systems coupled to gapped ℤ_2 gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting IsingboxtimesIsing̅ to toric-code order in the Choi state and yielding intrinsically mixed-state topological order upon unfolding. More interestingly, at a temporal interface between topological and trivial Kitaev states, a Chern-number mismatch enforces a gapless Majorana mode. Dephasing then drives a mixed-state topological transition at which the gapless mode develops emergent 𝒩=1 supersymmetry. Our Monte Carlo simulations yield ν=1.27(3) and η_b≃η_f≃0.40, consistent with the exact supersymmetric values 5/4 and 2/5. The supersymmetric partners are fractionalized and appear physically as distinct gauge-invariant spin strings, providing concrete observables for future experiments.
ER -