Fate of the non-Abelian Moore–Read manifold under the non-Hermitian skin effect

This paper investigates how non-Abelian topological order—specifically the Moore-Read Pfaffian state—responds to non-Hermitian perturbations. While non-Hermitian physics often leads to the non-Hermitian skin effect (where eigenstates accumulate at boundaries), it remains unclear if fractionalized topological states can survive this deformation or if the skin effect destroys their characteristic long-range entanglement structure.

The authors construct a Moore-Read fractional Chern insulator on a kagome lattice using a three-body interaction that stabilizes the state at filling factor ν=1/2. They introduce a nonreciprocal hopping term (an imaginary gauge shift) that preserves lattice translation but generates the non-Hermitian skin effect under open boundary conditions. To diagnose the state, they use the biorthogonal particle-entanglement spectrum (PES), checking if the (2,4)-admissible counting rule—the standard fingerprint of Moore-Read order—remains locked to the clean reference values as the nonreciprocity parameter γ increases.

The study demonstrates that the non-Abelian Moore-Read manifold is robust against non-Hermitian deformation up to a finite, size-dependent threshold. Across system sizes N=16, 20, and 24, the PES counting remains perfectly locked to the clean reference values over a finite window of γ. The authors confirm that the system maintains its topological fingerprint even as the single-particle states exhibit the skin effect. Beyond a geometry-dependent threshold, the entanglement gap closes, and the counting destabilizes. Interestingly, the authors find that an Abelian Laughlin state in the same lattice is more robust than the non-Abelian Moore-Read state, suggesting that non-Abelian order may have a lower tolerance for non-Hermitian deformation.

This work provides the first explicit diagnostic of a non-Abelian topological manifold under non-Hermitian conditions. It bridges the gap between fractionalized topological order and non-Hermitian physics, showing that topological protection can persist even when the underlying single-particle spectrum is significantly altered by the skin effect. This suggests that non-Abelian states could potentially be realized or manipulated in driven, dissipative, or non-reciprocal quantum systems.