A numerical study of an interacting kagome-lattice model found that a Moore-Read pattern remained visible across a finite range of non-Hermitian deformation, but its particle-entanglement fingerprint then broke down. In the largest calculation, with N = 24 lowest-band orbitals, the counted levels held at 9,282 through gamma <= 0.74. The fingerprint delocked in the bracket (0.74, 0.75], before a non-host momentum sector entered the lowest six in the later bracket (0.76, 0.77]. The result points to a finite window of persistence, not an unlimited tolerance.
What the model changed.
The document is an arXiv v1 preprint dated 26 August 2026. It asks how the skin effect changes a fractionalized, topologically ordered ground state. The deformation preserves translation symmetry while making hopping along one lattice direction nonreciprocal: right- and left-moving amplitudes differ by exponential factors, represented in momentum space by shifting k1 to k1 plus i gamma. The interaction is purely real and three-body, with U2 = 0 and U3 = 1; the authors describe it as a lattice analogue of the Moore-Read three-body parent pseudopotential.
A finite-size numerical test.
The main Moore-Read sequence used N = 16, 20 and 24 lowest-band orbitals on 4 x 4, 5 x 4 and 6 x 4 tori. The authors computed the complex spectrum by exact diagonalization in each momentum sector, using dense solvers for N = 16 and 20 and a warm-started sparse Krylov solver for N = 24.
The fingerprint was a counting rule.
The main test was the particle-entanglement spectrum, or PES, a diagnostic built from a reduced many-particle state. It counts PES levels below a chosen entanglement gap and compares that number with the configurations allowed by the (2, 4) rule. The primary calculation used a four-particle cut, with a six-particle cut as a cross-check. The researchers treated a stable match as the operational fingerprint of the Moore-Read manifold.
A clean starting point.
Before the deformation, the Hermitian point at gamma = 0 supplied a clean reference: a sixfold near-degenerate ground-state manifold at the reported sizes. At N = 24, those states occupied momentum sectors 0 and 12, and the gap separating the manifold from higher states was 7.2 times its internal width. Separate odd-filling checks found the tracked Ising doublet still paired and separated through gamma <= 0.6. There was a warning about simple energy sorting, however: near gamma = 0.5, the Nf = 7 doublet was temporarily overtaken in the global ordering by real energy.
Persistence across sizes.
Across the main sequence, the PES counts remained at 1,308 for N = 16 through gamma <= 0.55, 3,965 for N = 20 through gamma <= 0.65, and 9,282 for N = 24 through gamma <= 0.74. At N = 16, the result survived an audit of all 15 combinations formed from three reduced operators and five ways of reading the spectrum: every combination returned 1,308 at gamma = 0, 0.50 and 0.55. The energy separation also did not simply vanish in the central range: at N = 24, the all-sector gap to the seventh state rose from 6.94 x 10^-3 at gamma = 0 to 7.41 x 10^-3 at gamma = 0.6.
When the signal gave way.
The eventual failure of the PES pattern was marked by a sharp collapse of the reference-rank entanglement gap. From the survival-window edge to the first delocked sample, the gap fell by factors of 194 at N = 16, 7.5 x 10^11 at N = 20 and 1,400 at N = 24. At N = 24, the branch history also became harder to read: a pair in sector 0 turned into complex conjugates inside the delocking bracket. The continuation at gamma = 0.75 was ambiguous, but both tested continuations were delocked at gamma = 0.76, 0.77 and 0.80.
A longer-lived Abelian comparison.
A same-lattice Abelian Laughlin control lasted longer under the particular comparison. With N = 24 and Nf = 8 in a two-body model, its (1, 3) counting stayed at 2,730 through gamma = 1.0, while the Moore-Read count delocked between 0.74 and 0.75. That is a difference between the tested setups, not evidence that Abelian order is generally more stable: the comparison changes the filling, fermion number and interaction order.
Paper data and sources
Original title: Fate of the non-Abelian Moore-Read manifold under the non-Hermitian skin effect
Authors: Jiaxuan Guo, Simin Nie, Xiting Zhang, Fritz B. Prinz
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text