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 ${\rm Ising}\boxtimes\overline{\rm{Ising}}$ 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 $ν=1.27(3)$ and $η_b\simeqη_f\simeq0.40$, 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.

The paper asks how decoherence changes non-Abelian topological order and whether it can produce supersymmetric mixed-state criticality. It studies flux-preserving bond dephasing of the chiral Kitaev honeycomb ground state. Vectorization maps the channel to interactions between time-reversed Majorana copies; an exact auxiliary-field decomposition yields nonnegative Monte Carlo weights without Trotter error. In the normalized vectorized density matrix, increasing dephasing condenses the inter-copy boson $\psi\bar\psi$, changing doubled-Ising order to toric-code order. For $J_x=J_y=J_z=1$ and $\kappa=0.5$, Wilson-string finite-size scaling gives $p_c^{(2)}=0.16687(8)$, $\nu=1.011(16)$ and $\eta=0.246(11)$, consistent with two-dimensional Ising criticality. Unfolding the maximal-dephasing endpoint gives intrinsically mixed-state topological order with a transparent fermion. A distinct calculation uses strange correlators between topological and trivial reference states. Their Chern-number mismatch supplies gapless Majorana modes at a temporal interface. Dephasing drives this interface to a proposed tricritical-Ising endpoint with emergent $\mathcal N=1$ supersymmetry. Simulations up to $L=57$ give $p_c=0.24526(6)$, $\nu=1.27(3)$, $\eta_b=0.405(6)$ and $\eta_f=0.395(21)$, consistent with $5/4$ and $2/5$. Bosonic and fermionic partners are probed by distinct gauge-invariant spin strings; their estimated anisotropies also agree. The exponent $5/4$ applies to the symmetry-constrained dephasing trajectory, not generic tricritical-Ising tuning. The finite-dephasing mixed-state phase assignment assumes no intervening transition before maximal dephasing. Persistence beyond the integrable, flux-conserving setting is anticipated only while visons remain gapped and gauge fluctuations introduce no additional relevant perturbations.