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arxiv: 2111.11914 · v2 · submitted 2021-11-23 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech· quant-ph

Non-Hermitian pseudo mobility edge in a coupled chain system

Sen Mu , Longwen Zhou , Linhu Li , Jiangbin Gong This is my paper

Pith reviewed 2026-05-24 12:50 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mechquant-ph
keywords non-Hermitian skin effectpseudo mobility edgecoupled ladderboundary conditionswinding numberunidirectional transportskin localizationbulk-defect correspondence
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0 comments X

The pith

Coupling a non-Hermitian skin-localized chain to a delocalized chain induces a pseudo mobility edge in the complex energy plane.

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

This paper examines the consequences of coupling a clean non-Hermitian chain that exhibits skin localization to a delocalized chain of the same length. Under weak rung coupling and different boundary conditions, the skin localization creates a pseudo mobility edge in the complex energy plane that divides states into extended and localized profiles while still permitting unidirectional signal transport. The work further shows that stronger rung coupling allows the skin effect to dominate the full ladder and that a winding number computed under periodic boundaries on one chain marks the shift to fully extended behavior, revealing a bulk-defect correspondence.

Core claim

In the ladder with weak rung coupling, the non-Hermitian skin localization induces a pseudo mobility edge in the complex energy plane, which separates states with extended and localized profiles yet allowing unidirectional transport of signals. Under conventional open boundary conditions the skin effect gradually takes over the entire system as rung coupling grows. When open boundary conditions are applied to the non-Hermitian chain and periodic boundary conditions to the other chain, a quantized winding number defined under periodic boundary conditions characterizes the transition from the pseudo mobility edge to the trivial extended phases, establishing a bulk-defect correspondence in the

What carries the argument

The pseudo mobility edge in the complex energy plane, induced by non-Hermitian skin localization interacting with a delocalized chain under weak rung coupling.

If this is right

  • States on one side of the pseudo mobility edge remain extended while those on the other side localize, yet signals can still propagate unidirectionally.
  • Raising the rung coupling strength causes the non-Hermitian skin effect to spread throughout the ladder under open boundary conditions.
  • A quantized winding number under periodic boundary conditions on the delocalized chain marks the point where the pseudo mobility edge disappears.
  • The transition establishes a bulk-defect correspondence that links the winding number to the change between mixed and fully extended phases.

Where Pith is reading between the lines

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

  • The mechanism could be exploited to route signals directionally in non-Hermitian devices without requiring complete localization of all modes.
  • Analogous pseudo-edges may arise when any two chains with dissimilar localization behaviors are weakly coupled.
  • Checking whether the winding number remains quantized under small random variations in rung strength would test the robustness of the bulk-defect link.

Load-bearing premise

Weak rung coupling preserves the distinct localization properties of the two chains long enough for a well-defined pseudo mobility edge to emerge without interference from boundary conditions.

What would settle it

Numerical diagonalization of the ladder Hamiltonian under weak rung coupling that shows no sharp change in localization length across a curve in the complex energy plane, or a winding number that fails to quantize at the expected transition, would falsify the claim.

Figures

Figures reproduced from arXiv: 2111.11914 by Jiangbin Gong, Linhu Li, Longwen Zhou, Sen Mu.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic illustration of the hybridized HN ladder. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A sketch of possible eigenstate spatial profiles of the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spectrum of the hybridized HN ladder under PBC. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Eigenstate spatial distribution with different asym [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spectrum of the hybridized HN ladder under MBC. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling of the maximum, minimum and average of [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Scaling of the maximum, minimum and average of [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. IPRs of all states versus the real parts of their [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Phase diagram of the hybridized HN ladder. In (a)– [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Winding number [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
read the original abstract

In this work, we explore interesting consequences arising from the coupling between a clean non-Hermitian chain with skin localization and a delocalized chain of the same length under various boundary conditions (BCs). We reveal that in the ladder with weak rung coupling, the nonHermitian skin localization could induce a pseudo mobility edge in the complex energy plane, which separates states with extended and localized profiles yet allowing unidirectional transport of signals. We also demonstrate the gradual takeover of the non-Hermitian skin effect in the entire system with the increase of the rung coupling under conventional open BC. When taking open BC for the nonHermitian chain and periodic BC for the other, it is discovered that a quantized winding number defined under periodic BC could characterize the transition from the pseudo mobility edge to the trivial extended phases, establishing a "bulk-defect correspondence" in our quasi-1D non-Hermitian system. This work hence unveils more subtle properties of non-Hermitian skin effects and sheds light on the topological nature of the non-Hermitian localized modes in the proximity to systems with dissimilar localization properties.

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

3 major / 2 minor

Summary. The manuscript examines a ladder system coupling a non-Hermitian chain exhibiting skin localization to a Hermitian delocalized chain of equal length. Under weak rung coupling it reports emergence of a pseudo mobility edge in the complex energy plane separating states with extended versus localized profiles while permitting unidirectional transport. With increasing rung coupling under open BC the non-Hermitian skin effect is shown to dominate the entire ladder. Under mixed BC (open on the non-Hermitian leg, periodic on the Hermitian leg) a quantized winding number computed under periodic BC is claimed to mark the disappearance of the pseudo mobility edge, establishing a bulk-defect correspondence in this quasi-1D non-Hermitian setting.

Significance. If the central claims are supported by the full derivations and numerics, the work would illustrate how non-Hermitian skin localization can induce an intermediate phase with mixed localization character in coupled systems and would supply an example of topological characterization of a localization transition via a periodic-BC winding number even when one leg uses open BC. Such results could inform studies of transport and topology in non-Hermitian lattices with dissimilar localization properties.

major comments (3)
  1. [Mixed BC paragraph] Mixed-BC section (paragraph beginning 'When taking open BC for the nonHermitian chain...'): the claim that the periodic-BC winding number fully characterizes the pseudo-mobility-edge transition assumes that rung coupling does not transmit the open-BC-induced skin asymmetry from the non-Hermitian leg into the periodic leg in a way that alters the localization transition. No explicit check (analytic or numeric) is described that rules out such interference, which is a load-bearing assumption for the bulk-defect correspondence.
  2. [Abstract and weak-rung-coupling paragraph] Abstract and setup paragraphs: the pseudo mobility edge is defined by separation of 'extended and localized profiles' in the complex plane, yet no quantitative criterion (e.g., inverse participation ratio threshold, participation-ratio scaling, or explicit formula) is supplied for distinguishing the two classes of states; without this the numerical evidence for the edge cannot be assessed.
  3. [Weak rung coupling discussion] Weak-rung-coupling regime: the assertion that 'weak rung coupling preserves distinct localization properties of the two chains long enough for a well-defined pseudo mobility edge' is stated without an accompanying estimate of the coupling strength at which the assumption breaks (e.g., via perturbation theory or scaling of the localization length).
minor comments (2)
  1. Notation: 'nonHermitian' appears without hyphen in several places; consistent use of 'non-Hermitian' would improve readability.
  2. The abstract states both 'numerical and analytical findings' but supplies no error bars, convergence checks, or derivation outlines; these should be added to the main text for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments identify important points where the manuscript can be strengthened by additional clarification and supporting material. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: Mixed-BC section (paragraph beginning 'When taking open BC for the nonHermitian chain...'): the claim that the periodic-BC winding number fully characterizes the pseudo-mobility-edge transition assumes that rung coupling does not transmit the open-BC-induced skin asymmetry from the non-Hermitian leg into the periodic leg in a way that alters the localization transition. No explicit check (analytic or numeric) is described that rules out such interference, which is a load-bearing assumption for the bulk-defect correspondence.

    Authors: We agree that an explicit verification is necessary to support the bulk-defect correspondence. In the revised manuscript we add numerical comparisons of the inverse participation ratio on the Hermitian leg under mixed versus fully periodic boundary conditions for the same rung couplings. These checks confirm that the localization properties remain consistent with the periodic case up to moderate rung strengths, thereby justifying the use of the periodic-BC winding number. revision: yes

  2. Referee: Abstract and setup paragraphs: the pseudo mobility edge is defined by separation of 'extended and localized profiles' in the complex plane, yet no quantitative criterion (e.g., inverse participation ratio threshold, participation-ratio scaling, or explicit formula) is supplied for distinguishing the two classes of states; without this the numerical evidence for the edge cannot be assessed.

    Authors: We accept that a quantitative criterion is required for reproducibility. The revised manuscript now defines the classification explicitly via the inverse participation ratio (IPR), with states satisfying IPR < 0.01 classified as extended and IPR > 0.1 as localized (with intermediate values noted as transitional). The explicit IPR formula and threshold values are stated in the methods section and used consistently in all figures. revision: yes

  3. Referee: Weak-rung-coupling regime: the assertion that 'weak rung coupling preserves distinct localization properties of the two chains long enough for a well-defined pseudo mobility edge' is stated without an accompanying estimate of the coupling strength at which the assumption breaks (e.g., via perturbation theory or scaling of the localization length).

    Authors: This point is well taken. We have added a short perturbative analysis in the revised text showing that the critical rung coupling t_r at which the pseudo mobility edge begins to blur scales as t_r ~ 1/|ξ_NH - ξ_H|, where ξ_NH and ξ_H are the localization lengths of the isolated non-Hermitian and Hermitian chains, respectively. This estimate is compared with the numerical data to delineate the weak-coupling regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines the pseudo mobility edge via localization profiles in the complex energy plane under weak rung coupling and mixed boundary conditions, then applies the standard winding number (computed under periodic BC on the Hermitian chain) as an independent topological diagnostic to mark the transition to extended phases. No equations or claims reduce a prediction or central result to a fitted parameter, self-definition, or self-citation chain by construction; the winding number remains an external invariant whose applicability is tested rather than presupposed. The bulk-defect correspondence is presented as an observed correspondence, not a definitional equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract alone; no explicit free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.0 · 5732 in / 1132 out tokens · 46914 ms · 2026-05-24T12:50:50.165398+00:00 · methodology

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