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arxiv: 2601.14754 · v2 · submitted 2026-01-21 · ❄️ cond-mat.dis-nn · quant-ph

Anomalous Localization and Mobility Edges in Non-Hermitian Quasicrystals with Disordered Imaginary Gauge Fields

Guolin Nan , Zhijian Li , Feng Mei , Zhihao Xu This is my paper

Pith reviewed 2026-05-16 12:33 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn quant-ph
keywords non-Hermitian localizationquasicrystalsmobility edgeskin effectAubry-André-Harper modeldisordered gauge fieldspectral winding
0
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The pith

A Bernoulli imaginary gauge field in a non-Hermitian Aubry-André-Harper chain produces an anomalous transition from erratic skin-effect states to fully localized states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The work considers a one-dimensional non-Hermitian Aubry-André-Harper model whose imaginary gauge field is drawn from a Bernoulli distribution together with quasiperiodic onsite potentials. In the nearest-neighbor hopping limit the system undergoes a sharp change from a phase of erratic non-Hermitian skin effect to a phase of complete localization. Both phases have vanishing fractal dimension, yet they are cleanly separated by the Lyapunov exponent and by the fluctuation of each eigenstate’s center of mass. Adding weak next-nearest-neighbor hopping turns the same critical point into an anomalous mobility edge that separates Anderson-localized states from macroscopic skin-effect accumulation states. The distinction is visible in the change of spectral winding under periodic boundaries and in the directional drift of wave packets.

Core claim

In the nearest-neighbor limit the model exhibits an anomalous transition from a fully erratic non-Hermitian skin effect phase to a fully localized phase. Although the fractal dimension vanishes on both sides of the transition, the Lyapunov exponent and the variance of the eigenstate center of mass sharply distinguish the two regimes. With weak next-nearest-neighbor hopping the transition point functions as a mobility edge separating Anderson-localized states from ENHSE-type states whose spectral winding and wave-packet dynamics differ from those of the Hermitian generalized Aubry-André-Harper model.

What carries the argument

The one-dimensional non-Hermitian Aubry-André-Harper chain with Bernoulli-distributed imaginary gauge field, whose nearest-neighbor limit hosts the ENHSE-to-localized transition diagnosed by Lyapunov exponents and center-of-mass fluctuations.

If this is right

  • The transition coincides with a change from complex to real eigenvalues under periodic boundary conditions.
  • Spectral winding number changes from nontrivial to trivial across the transition.
  • The anomalous mobility edge remains at the same parameter location as the Hermitian generalized Aubry-André-Harper mobility edge.
  • Single disorder realizations display winding-dependent wave-packet drift while full disorder averaging restores Hermitian-like transport.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Replacing the Bernoulli distribution with a smooth random distribution would likely smear the sharp distinction between the two phases.
  • The same Lyapunov-exponent and center-of-mass diagnostics could be applied to two-dimensional non-Hermitian quasicrystals to look for analogous anomalous mobility edges.
  • Cold-atom or photonic-lattice experiments with engineered gain-loss profiles could directly measure the predicted winding-dependent drift of wave packets.

Load-bearing premise

The transition and mobility edge rely on the imaginary gauge field obeying a Bernoulli distribution and on strictly nearest-neighbor hopping; any other distribution or longer-range hopping can remove the anomalous character.

What would settle it

Compute the Lyapunov exponent and center-of-mass fluctuation across the critical point for many finite realizations in the nearest-neighbor model; if these quantities vary continuously rather than jump, the claimed anomalous transition is ruled out.

Figures

Figures reproduced from arXiv: 2601.14754 by Feng Mei, Guolin Nan, Zhihao Xu, Zhijian Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Representative eigenstate profiles [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mean fractal dimension [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Eigenenergy spectra under PBCs and OBCs at (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a,b) Winding number [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Localization phase diagram under PBCs in the (Re( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Energy spectra under different boundary conditions fo [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Maximum imaginary part of PBC eigenenergies [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Time evolution of the wave-function profile [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Disorder-averaged wave-packet dynamics. Disorder [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-Andr\'{e}-Harper chain with a Bernoulli imaginary gauge field and quasiperiodic onsite modulation. In the nearest-neighbor limit, we identify an anomalous transition from a fully erratic non-Hermitian skin effect (ENHSE) phase to a fully localized phase. Although the fractal dimension vanishes in both regimes, the Lyapunov exponent and the fluctuation of the eigenstate center of mass sharply distinguish them. For generic finite-size realizations, this transition is further accompanied by a complex-to-real spectral change under periodic boundary conditions and a change of spectral winding from nontrivial to trivial. With weak next-nearest-neighbor hopping, we uncover an anomalous mobility edge at the same location as in the Hermitian generalized Aubry-Andr\'{e}-Harper model, but separating Anderson-localized states from ENHSE-type macroscopic-accumulation states rather than extended states. We further show that this anomalous localization structure is reflected in spectral winding and wave-packet dynamics: single realizations exhibit winding-dependent drift, winding-resolved averaging preserves opposite directional responses, and full disorder averaging largely restores Hermitian-like transport. Our results establish practical diagnostics of anomalous localization and mobility edges in non-Hermitian quasicrystals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. This paper examines a non-Hermitian Aubry-André-Harper chain with a Bernoulli imaginary gauge field and quasiperiodic onsite modulation. In the nearest-neighbor limit, it identifies an anomalous transition from a fully erratic non-Hermitian skin effect (ENHSE) phase to a fully localized phase. Although the fractal dimension vanishes in both regimes, the phases are distinguished by the Lyapunov exponent and eigenstate center-of-mass fluctuation. The transition is accompanied by a complex-to-real spectral change and a change in spectral winding from nontrivial to trivial under periodic boundaries. With weak next-nearest-neighbor hopping, an anomalous mobility edge appears at the same location as in the Hermitian case but separates Anderson-localized states from ENHSE-type states. The work further connects these features to spectral winding and wave-packet dynamics under different averaging schemes.

Significance. If the reported distinctions survive the thermodynamic limit, the manuscript would provide useful, independently defined diagnostics (Lyapunov exponent, center-of-mass fluctuation, spectral winding) for identifying anomalous localization phases in non-Hermitian quasicrystals that differ from both Hermitian Anderson localization and conventional skin-effect phenomenology. The explicit links to wave-packet dynamics and averaging procedures add practical value for experimental realization.

major comments (1)
  1. [Abstract and nearest-neighbor results section] Abstract and nearest-neighbor results section: the central claim that the Lyapunov exponent and eigenstate center-of-mass fluctuation sharply distinguish the ENHSE phase from the localized phase rests on data for generic finite-size realizations. No explicit finite-size scaling analysis or L→∞ extrapolation of either quantity is presented, leaving open the possibility that the apparent sharpness is a finite-size artifact arising from the 'erratic' character of the skin effect.
minor comments (2)
  1. [Abstract] The acronym ENHSE is introduced in the abstract without expansion; spell out 'erratic non-Hermitian skin effect' on first use and ensure consistent definition in the main text.
  2. [Methods or numerical details section] Clarify the precise numerical definition of the eigenstate center-of-mass fluctuation (e.g., variance formula) and the system sizes used for the reported Lyapunov exponents to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major concern regarding finite-size effects below and have revised the manuscript to include additional analysis.

read point-by-point responses

  1. Referee: [Abstract and nearest-neighbor results section] Abstract and nearest-neighbor results section: the central claim that the Lyapunov exponent and eigenstate center-of-mass fluctuation sharply distinguish the ENHSE phase from the localized phase rests on data for generic finite-size realizations. No explicit finite-size scaling analysis or L→∞ extrapolation of either quantity is presented, leaving open the possibility that the apparent sharpness is a finite-size artifact arising from the 'erratic' character of the skin effect.

    Authors: We agree that the distinction between the ENHSE and localized phases would be more robustly established with explicit finite-size scaling. The current results are shown for finite L with multiple generic realizations, where the Lyapunov exponent and center-of-mass fluctuation exhibit a clear jump at the transition. To address the concern directly, the revised manuscript adds a finite-size scaling analysis (new figure and discussion in the nearest-neighbor section) for L up to several hundred sites. This confirms that the sharpness persists without rounding as L increases, with the Lyapunov exponent remaining near zero on the ENHSE side and acquiring a finite value on the localized side, and the fluctuation showing a corresponding drop. The transition location is stable under this scaling, indicating it is not a finite-size artifact. We have also updated the abstract to note the added scaling support. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central diagnostics are independently defined

full rationale

The paper identifies the ENHSE-to-localized transition and anomalous mobility edge via direct numerical evaluation of the Lyapunov exponent, eigenstate center-of-mass fluctuation, fractal dimension, spectral winding, and wave-packet dynamics. None of these quantities is defined in terms of the transition location or fitted to it; the fractal dimension vanishing on both sides is reported as an observation, not a redefinition. No load-bearing self-citation chain or ansatz smuggling is required for the distinction, and the nearest-neighbor Bernoulli case is treated as a specific parameter regime rather than a tautological input. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the standard Aubry-André-Harper quasiperiodic potential, the assumption that the imaginary gauge field is Bernoulli-distributed, and the use of Lyapunov exponents and spectral winding as phase diagnostics; these are domain-standard ingredients rather than new postulates.

free parameters (1)
  • imaginary gauge field amplitude
    The strength of the Bernoulli-distributed imaginary term controls the location of the anomalous transition and is a tunable parameter in the model.
axioms (1)
  • domain assumption The Lyapunov exponent and eigenstate center-of-mass fluctuation are independent of the fractal dimension and can be used to distinguish phases when the latter vanishes.
    Invoked to separate the ENHSE and localized regimes despite zero fractal dimension in both.
invented entities (1)
  • erratic non-Hermitian skin effect (ENHSE) no independent evidence
    purpose: Label for the phase in which eigenstates exhibit macroscopic boundary accumulation with erratic spatial structure.
    New descriptive term introduced for the observed non-Hermitian skin-effect regime under disordered gauge fields.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Erratic Liouvillian Skin Localization and Subdiffusive Transport

    quant-ph 2026-02 unverdicted novelty 7.0

    Globally reciprocal Liouvillian systems show erratic localization coexisting with subdiffusive transport, unlike ballistic transport in equivalent Hamiltonian models.

Reference graph

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