AI 中文总结
研究非阿贝尔Moore-Read分数量子陈绝缘体在非厄米皮肤效应下的演化，通过双正交粒子-纠缠计数诊断其序，发现其计数在一定非互易窗口内稳定，超过阈值后失稳，而阿贝尔Laughlin态计数更鲁棒。
AI 中文摘要
我们研究了非阿贝尔Moore-Read分数量子陈绝缘体，该体系处于平移不变、非互易的形变下，这种形变在开放边界条件下会产生非厄米皮肤效应。该模型结合了虚规范Hatano-Nelson形变与 kagome 晶格三体相互作用，旨在稳定填充因子ν=1/2处的Moore-Read序。我们的主要诊断工具是六重简并Moore-Read流形的双正交(2,4)可容许粒子-纠缠计数，这是Moore-Read序的标准指纹。在三种体系尺寸（N=16、20、24）下，在有限非互易窗口（γ分别≤0.55、0.65、0.74）内，该计数锁定于无杂质参考值1308、3965和9282，且具有正的参考秩纠缠能隙。在每个报告的窗口内，所测试的谱读数不会改变计数；对于N=16，三种约化密度算符下计数也保持不变，所有15种组合均返回1308。在测试范围γ≤0.6内，N_f为偶数时的六重模式与绝热跟踪的伊辛奇二重态仍保持分离。超过与几何相关的阈值后，瞬时最低六重参考秩能隙急剧下降，其计数变得不稳定。在N=24时，在去锁定区间内的一个窄区间内，0区的一对分支成为复共轭；在测试的PES点γ=0.76、0.77和0.80处，该区间的两种延拓均被去锁定。同一晶格上的阿贝尔ν=1/3 Laughlin实现的计数可保持到γ=1.0，因此其计数更为鲁棒。在环面上，本征态保持扩展；在开放边界条件下，左右态分别局域于相对的边缘，而双正交粒子-纠缠谱在虚规范相似变换下不变，因此环面与开放圆柱分别在周期边界和开放边界下探测相同的形变。
英文摘要
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 $ν=1/2$. 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 $γ\le0.55$, $0.65$, 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 $γ\le0.6$. 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 $γ=0.76$, $0.77$, and $0.80$. A same-lattice Abelian $ν=1/3$ Laughlin realization retains its counting to $γ=1.0$, 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.
