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

Abstract:We study a non-Abelian Moore-Read fractional Chern insulator under a translation-preserving, nonreciprocal deformation that generates the non-Hermitian skin effect under open boundaries. The model combines the imaginary-gauge Hatano-Nelson deformation with a kagome-lattice three-body interaction designed to stabilize Moore-Read order at $\nu=1/2$. Our primary diagnostic is the biorthogonal $(2,4)$-admissible particle-entanglement counting of the sixfold Moore-Read manifold, the standard Moore-Read fingerprint. Across three sizes ($N=16,20,24$), the counting locks to the clean references 1308, 3965, and 9282 over finite nonreciprocity windows through $\gamma\le0.55$, $0.65$, and $0.74$, respectively, with positive reference-rank entanglement gaps. Within every reported window the count is unchanged by the spectral readings tested; at $N=16$ it is also unchanged across three reduced density operators, with all 15 combinations returning 1308. The sixfold pattern for even $N_f$ and the adiabatically tracked Ising-odd doublet remain separated over the tested range $\gamma\le0.6$. Beyond a geometry-dependent threshold the instantaneous-lowest-six reference-rank gap drops sharply and its counting destabilizes. At $N=24$ a sector-0 branch pair becomes complex conjugate over a narrow interval inside the delocking bracket; both continuations through the interval are delocked at the tested PES points $\gamma=0.76$, $0.77$, and $0.80$. A same-lattice Abelian $\nu=1/3$ Laughlin realization retains its counting to $\gamma=1.0$, so its counting is the more robust. On the torus the eigenstates remain extended; under open boundaries the right and left states skin-localize at opposite edges while the biorthogonal particle-entanglement spectrum is invariant under the imaginary-gauge similarity, so the torus and the open cylinder probe the same deformation under periodic and open boundaries.

Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2608.25816 [cond-mat.str-el]

(or arXiv:2608.25816v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2608.25816 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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