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 ${\mathbb{Z}}_2$ gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting $\mathrm{Ising}⊠\overline{\mathrm{Ising}}$ 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 $\mathcal{N}=1$ supersymmetry. Our Monte Carlo simulations yield $\nu =1.27(3)$ and ${\eta }_b\simeq {\eta }_f\simeq 0.40$, 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.

arXiv comment4.3 pages + supplemental material, 3 figures