Exceptional-point-constrained locking of boundary-sensitive topological transitions in chiral non-Hermitian SSH-type lattices

Huimin Wang; Yanxin Liu; Zhihao Xu; Zhijian Li

arxiv: 2603.25451 · v3 · submitted 2026-03-26 · ⚛️ physics.optics · quant-ph

Exceptional-point-constrained locking of boundary-sensitive topological transitions in chiral non-Hermitian SSH-type lattices

Huimin Wang , Yanxin Liu , Zhijian Li , Zhihao Xu This is my paper

Pith reviewed 2026-05-15 06:50 UTC · model grok-4.3

classification ⚛️ physics.optics quant-ph

keywords non-Hermitian topologyexceptional pointsSSH latticepoint-gap windingnon-Bloch bandsboundary modeschiral symmetrytopological transitions

0 comments

The pith

EP-constrained sweeps lock PBC and OBC topological transitions in non-Hermitian SSH lattices

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

In non-Hermitian systems topological transitions under periodic and open boundary conditions are generally governed by different spectra and therefore do not coincide. This paper shows that in a class of chiral non-Hermitian SSH-type lattices, parameter paths that keep a zero-energy Bloch degeneracy present throughout the sweep force the two transitions to occur at the same point. The persistence of this degeneracy, which is exceptional in the non-Hermitian setting, produces the locking: a change in point-gap winding under periodic boundaries now marks the non-Bloch real-line-gap transition under open boundaries and the associated change in zero-energy boundary modes. Closed-form results are given for an extended two-band chain, while generalized Brillouin-zone numerics confirm the effect in generic two-band and four-band cases; unconstrained paths lack the locking.

Core claim

For chiral non-Hermitian Su-Schrieffer-Heeger type lattices, exceptional-point-constrained parameter evolutions lock the point-gap winding transition under periodic boundary conditions to the non-Bloch bulk real-line-gap transition under open boundary conditions at Re(E)=0. The locking holds because the zero-energy Bloch degeneracy persists along the entire sweep. In an analytically tractable limit the EP-constrained manifolds and both transition boundaries are obtained in closed form; away from the limit, generalized-Brillouin-zone calculations verify the correspondence for representative constrained sweeps while showing that isolated exceptional points or Hermitian degeneracies do not lock

What carries the argument

Exceptional-point-constrained parameter evolution that preserves a zero-energy Bloch degeneracy along the entire sweep

Load-bearing premise

A zero-energy Bloch degeneracy persists along the full parameter sweep in the non-Hermitian regime

What would settle it

A numerical sweep that maintains the zero-energy degeneracy throughout yet shows a PBC winding change without a corresponding OBC real-line-gap transition at Re(E)=0

read the original abstract

Topological transitions in non-Hermitian systems are generally boundary sensitive: a point-gap winding transition under periodic boundary condition (PBC) and a non-Bloch bulk real-line-gap transition under open boundary condition (OBC) at $\mathrm{Re}(E)=0$ are governed by different spectra and therefore need not coincide. Here we show, for a class of chiral non-Hermitian Su--Schrieffer--Heeger (SSH)-type lattices, that these two criticalities can be locked by an exceptional-point-constrained (EP-constrained) parameter evolution. The key requirement is not the occurrence of isolated exceptional points, but the persistence of a zero-energy Bloch degeneracy along the entire sweep, which is generically exceptional in the non-Hermitian regime. In an analytically tractable limit of an extended non-Hermitian SSH chain, the EP-constrained manifolds and both transition boundaries are obtained in closed form, making the locking explicit. Away from this limit, numerical generalized-Brillouin-zone (GBZ) calculations confirm the correspondence for representative constrained sweeps, whereas unconstrained paths show that isolated exceptional points or Hermitian degeneracies do not enforce locking. We further verify the mechanism in a spinful four-band extension with branch-resolved GBZs, including strongly branch-imbalanced regimes. These results establish a path-dependent diagnostic principle: along EP-constrained sweeps in this SSH-type class, changes in PBC point-gap winding can indicate OBC non-Bloch bulk real-line-gap transitions and the corresponding changes in zero-energy boundary modes.

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.

Desk Editor's Note private letter to a colleague

The paper shows how to lock PBC point-gap winding transitions to OBC non-Bloch real-line-gap transitions in chiral non-Hermitian SSH lattices by keeping a zero-energy Bloch degeneracy exceptional along the entire parameter path.

read the letter

The core result is that in this class of models, an EP-constrained sweep forces the two boundary-sensitive criticalities to coincide because the zero-energy degeneracy persists throughout. They derive the constrained manifolds and transition lines in closed form for the extended non-Hermitian SSH limit, then confirm the locking with GBZ numerics on representative paths and show that unconstrained paths or isolated EPs do not produce the same effect. The four-band spinful extension with branch-resolved GBZs adds a useful check in a more complex setting. This is genuinely new within the non-Hermitian SSH literature; the persistence condition is stated plainly and the counter-examples help isolate what actually matters. The analytical tractability in the simple limit is the strongest part. The numerical support is adequate for the claim but limited to selected paths without exhaustive scans or error bars, which leaves some room for doubt on robustness. The persistence of the degeneracy is presented as necessary, yet it remains a strong assumption that could break under perturbations not explored here. Overall the mechanism is internally consistent and the derivations stand on their own. This is for people already working on non-Hermitian topology and boundary effects in lattice models. It is narrow but concrete enough that a serious referee should see it, mainly to check the GBZ details and generality beyond the tractable limit.

Referee Report

1 major / 3 minor

Summary. The manuscript claims that in chiral non-Hermitian SSH-type lattices, exceptional-point-constrained parameter sweeps lock PBC point-gap winding transitions to OBC non-Bloch real-line-gap transitions (and associated zero-mode changes) at Re(E)=0. This locking occurs because a zero-energy Bloch degeneracy persists along the entire sweep. Closed-form expressions for the EP-constrained manifolds and both transition boundaries are derived in an analytically tractable limit of an extended non-Hermitian SSH chain; GBZ numerics confirm the correspondence for representative constrained paths (with counter-examples for unconstrained paths) and extend to a spinful four-band model with branch-resolved GBZs.

Significance. If the central claim holds, the work supplies a concrete path-dependent diagnostic that connects PBC winding changes to OBC non-Bloch bulk transitions in this SSH class, with the persistence of the zero-energy degeneracy as the enabling mechanism. The closed-form results in the tractable limit and the reproducible GBZ checks constitute clear strengths that allow direct verification of the locking without fitted parameters.

major comments (1)

[Analytically tractable limit] The central locking mechanism rests on persistence of the zero-energy Bloch degeneracy along the full EP-constrained path. While the abstract states this requirement explicitly and the tractable-limit derivation obtains the manifolds in closed form, the manuscript should add an explicit verification (perhaps as a short lemma or appendix) that the degeneracy condition is identically satisfied on the derived manifolds rather than imposed separately.

minor comments (3)

[Numerical verification] The GBZ plots for the four-band extension would benefit from explicit labeling of the branch-resolved spectra and a brief statement of the numerical tolerance used to identify the real-line gap closing.
[Introduction] The counter-examples for unconstrained paths are mentioned but not cross-referenced to specific parameter values or figures; adding one or two explicit unconstrained trajectories alongside the constrained ones would make the contrast immediate.
Notation for the generalized Brillouin zone and the point-gap winding number should be defined once in a dedicated paragraph before the first use to avoid ambiguity in the multi-band extension.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the constructive suggestion regarding the analytically tractable limit. We address the comment below.

read point-by-point responses

Referee: [Analytically tractable limit] The central locking mechanism rests on persistence of the zero-energy Bloch degeneracy along the full EP-constrained path. While the abstract states this requirement explicitly and the tractable-limit derivation obtains the manifolds in closed form, the manuscript should add an explicit verification (perhaps as a short lemma or appendix) that the degeneracy condition is identically satisfied on the derived manifolds rather than imposed separately.

Authors: We agree that an explicit verification would strengthen the presentation of the locking mechanism. In the revised manuscript we add a short lemma in Appendix A. The lemma proves that the zero-energy Bloch degeneracy holds identically on the derived EP-constrained manifolds: it follows directly from the chiral symmetry of the extended non-Hermitian SSH Hamiltonian together with the closed-form expressions for the manifolds, without any separate imposition of the degeneracy condition. revision: yes

Circularity Check

0 steps flagged

No significant circularity; closed-form derivation stands independently

full rationale

The central claim is established by explicit closed-form solution of the EP-constrained manifolds and both transition boundaries in the analytically tractable extended non-Hermitian SSH limit. The persistence of the zero-energy Bloch degeneracy is introduced as an explicit necessary condition and used directly to derive the locking; it is not obtained by fitting, self-definition, or prior self-citation. GBZ numerics are presented only as confirmation for representative paths and counter-examples, not as the source of the result. No load-bearing step reduces to its own input by construction, and no uniqueness theorem or ansatz is imported via self-citation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on standard non-Hermitian band theory and GBZ formalism plus the new requirement of persistent zero-energy degeneracy; no new particles or forces are introduced.

free parameters (1)

hopping amplitudes in the extended non-Hermitian SSH chain
Model parameters swept along the constrained paths; their specific values define the analytically tractable limit.

axioms (1)

domain assumption Generalized Brillouin zone formalism accurately captures OBC spectra in non-Hermitian lattices
Invoked for all numerical verification of the locking.

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discussion (0)

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Works this paper leans on

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Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian ha miltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)

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J., Budich, J

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