Noise-induced decoherence-free zones for anyons

TL;DR

The paper develops a stochastic framework for abelian anyons in which the exchange phase is treated as a fluctuating parameter, leading to a statistics-dependent pure dephasing channel within a Lindblad master equation. By deriving the model from a distorted anyon algebra and promoting the exchange phase to a stochastic (and then quantum) process, the authors connect decoherence protection to the eigenstructure of a real symmetric correlation matrix $D_{ab}$, enabling decoherence-free subspaces and, under certain correlations, decoherence exceptional points. A striking result is the universality of the optimal statistical angle $\theta^*=\pi/2$ in the minimal two-site model, where the protected mode is maximally robust against dephasing independent of $D$. They further analyze multi-link extensions, showing how correlated noise and the cross-spectral properties $S_{ab}(0)$ determine protection and the possible emergence of non-normal Liouvillians and EPs. The framework offers practical design rules for preserving coherence in noisy anyonic systems and has relevance for ultracold-atom realizations and other platforms exploring fractional statistics.

Abstract

We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich--Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics--dependent dephasing channel, with rates determined by the eigenstructure of the real symmetric correlation matrix $D_{ab}$. The eigenvectors of $D$ select which collective exchange currents -- equivalently, which irreducible representations of the system -- are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at $θ^\star = π/2$, independent of the specific form of $D$. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.

Figures (2)

• Figure 1: Two sites connected by fluctuating paths with random phases $\phi_a(t)$ and $\phi_b(t)$. A correlation $D_{ab}$ between the two noise sources captures the strength of correlated environmental fluctuations.
• Figure 2: Dephasing rate scaled by exchange coupling, $\gamma_\phi(\theta)/J$, versus statistical phase $\theta$ for three representative correlation strengths: $\xi=0$, $\xi=0.5$, and $\xi=0.9$. All curves exhibit a universal minimum at $\theta^\star = \pi/2$, independent of $\xi$, demonstrating the robustness of the half-fermionic protection point. Rates are expressed in dimensionless units normalized by the exchange coupling $J$ (with $J=0.1$ in the underlying simulation).