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arxiv: 2606.13200 · v1 · pith:ZZKHEC24new · submitted 2026-06-11 · 🪐 quant-ph · cond-mat.mes-hall· cond-mat.stat-mech

Interference of critical dynamics associated with zero modes

Zhi-Han Zhang , Han-Chuan Kou , Peng Li This is my paper

Pith reviewed 2026-06-27 06:30 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hallcond-mat.stat-mech
keywords zero modescritical dynamicstopological phasesCreutz ladderquench dynamicsinterference patternsWKB analysisedge defects
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The pith

Closed quench paths through two critical points in generalized Creutz ladders produce ICDZM patterns in zero-mode transfer probability that either vanish or double in period when the path links two topologically nontrivial phases.

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

The paper examines interference of critical dynamics associated with zero modes in generalized Creutz ladders by driving the system along closed quench paths that cross two critical points in succession. It reports that the final zero-mode transfer probability exhibits path-dependent interference patterns, with the pattern vanishing or showing period doubling specifically when the path connects two topologically nontrivial phases. This behavior is traced to the interference phase that accumulates during the quench. The transfer probability appears experimentally as a deviation of the boundary particle number away from its initial fractional value because bulk modes blend into the edge during the critical dynamics. The work positions this probability and the associated edge defect as readable probes for the critical dynamics of topological zero modes.

Core claim

We study the interference of critical dynamics associated with zero modes (ICDZM) in the generalized Creutz ladders using closed quench paths that pass through two critical points successively. By reading out the final zero-mode transfer probability, we find rich ICDZM interference patterns dependent on the quench path. In particular, when the closed path links two topologically nontrivial phases, the ICDZM pattern may either vanish or exhibit period doubling. Within the framework of WKB analysis, this phenomenon is well clarified by the interference phase accumulated in the quench procedure. We also demonstrate that the zero-mode transfer probability can be detected by the deviation of the

What carries the argument

The accumulated interference phase along the closed quench path, extracted via WKB analysis, that controls whether the ICDZM pattern in zero-mode transfer probability vanishes or doubles.

If this is right

  • The zero-mode transfer probability appears as a deviation of boundary particle number from its initial fractional value due to bulk-mode blending.
  • The probability records both the ICDZM oscillation and anomalous defect production from non-closed paths.
  • ICDZM and the edge defect serve as probes for critical dynamics tied to topological zero modes.

Where Pith is reading between the lines

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

  • The same phase-accumulation mechanism could be tested in other one-dimensional topological models that support zero modes under analogous double-critical-point quenches.
  • Boundary density measurements in cold-atom realizations of ladder systems offer a direct route to extract the transfer probability without requiring full state tomography.
  • The distinction between vanishing and period-doubled patterns may provide a quench-based diagnostic for the relative topological character of the two phases being connected.

Load-bearing premise

The WKB analysis accurately captures the interference phase accumulated along the closed quench path without significant corrections from non-adiabatic or higher-order effects near the two critical points.

What would settle it

An experiment that measures zero-mode transfer probability for a closed quench path connecting two topologically nontrivial phases and finds neither vanishing nor period doubling in the oscillation pattern.

Figures

Figures reproduced from arXiv: 2606.13200 by Han-Chuan Kou, Peng Li, Zhi-Han Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram and quench protocols of the gener [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (e) still shows an ordinary ICD oscillation around the KZ background. This comparison between protocols 1 and 2 shows that the pair-occupation relation fixes the final redistribution inside the zero-mode pair, but it does not determine the visibility of ICDZM. A visible ICDZM oscillation also requires a sizable oscillatory part in p Z. Finally, we consider protocol 3, where µ is varied at fixed θ = π/2. Th… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Relation between the OBC energy gap and the PBC [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Deviations of the particle number produced in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between the zero-mode transfer prob [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

We study the interference of critical dynamics associated with zero modes (ICDZM) in the generalized Creutz ladders using closed quench paths that pass through two critical points successively. By reading out the final zero-mode transfer probability, we find rich ICDZM interference patterns dependent on the quench path. In particular, when the closed path links two topologically nontrivial phases, the ICDZM pattern may either vanish or exhibit period doubling. Within the framework of WKB analysis, this phenomenon is well clarified by the interference phase accumulated in the quench procedure. We also demonstrate that the zero-mode transfer probability can be detected by the deviation of the boundary particle number from its initial fractional value, which arises from the blending of bulk modes in the critical dynamics. As an edge defect, the zero-mode transfer probability captures both the ICDZM oscillation and the known anomalous defect production in a non-closed quench path. These results identify ICDZM and the corresponding edge defect as probes for critical dynamics associated with topological zero 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.

Referee Report

2 major / 2 minor

Summary. The manuscript studies interference of critical dynamics associated with zero modes (ICDZM) in generalized Creutz ladders along closed quench paths that successively traverse two critical points. The central observations are that the final zero-mode transfer probability exhibits path-dependent interference patterns, which can vanish or show period doubling when the path connects two topologically nontrivial phases; these features are attributed to the accumulated interference phase analyzed via WKB. The authors further show that the transfer probability appears as a deviation of the boundary particle number from its initial fractional value due to bulk-mode blending in the critical dynamics, and position the ICDZM pattern and associated edge defect as experimental probes for topological zero-mode critical dynamics.

Significance. If the central claims hold, the work supplies a concrete interference-based diagnostic for critical dynamics tied to topological zero modes and a practical detection route via boundary observables. The explicit linkage of pattern vanishing/period-doubling to a WKB phase and the identification of an edge defect that encodes both closed-path interference and open-path anomalous production are the main strengths.

major comments (2)
  1. [Abstract and WKB analysis] Abstract (WKB clarification paragraph) and associated analysis section: the statement that the vanishing or period-doubling 'is well clarified by the interference phase accumulated in the quench procedure' within the WKB framework is load-bearing for the central claim, yet the paths pass through gap-closing critical points where the instantaneous gap vanishes and the adiabatic/WKB assumption is violated; no explicit error bound, Landau-Zener correction estimate, or numerical benchmark against exact dynamics is provided to show that non-adiabatic corrections remain negligible for the chosen ramp speeds and paths.
  2. [Detection via boundary particle number] Section describing the boundary-particle-number detection: the claim that the zero-mode transfer probability is captured by the deviation of the boundary particle number from its initial fractional value relies on the blending of bulk modes, but the manuscript does not quantify how this deviation isolates the ICDZM contribution from other critical or non-critical bulk effects, nor does it compare the predicted deviation magnitude against the known anomalous defect production in the non-closed case.
minor comments (2)
  1. [Abstract] The acronym ICDZM is introduced without an explicit expansion on first use in the abstract.
  2. [Figures] Figure captions for the interference patterns should state the precise quench-path parameters and ramp protocol used, to allow direct comparison with the WKB phase formula.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the two major comments below and will revise the manuscript to incorporate the requested clarifications and supporting analyses.

read point-by-point responses

  1. Referee: [Abstract and WKB analysis] Abstract (WKB clarification paragraph) and associated analysis section: the statement that the vanishing or period-doubling 'is well clarified by the interference phase accumulated in the quench procedure' within the WKB framework is load-bearing for the central claim, yet the paths pass through gap-closing critical points where the instantaneous gap vanishes and the adiabatic/WKB assumption is violated; no explicit error bound, Landau-Zener correction estimate, or numerical benchmark against exact dynamics is provided to show that non-adiabatic corrections remain negligible for the chosen ramp speeds and paths.

    Authors: We agree that the WKB approximation is formally invalid exactly at the gap-closing points. The phase accumulation we invoke occurs in the gapped segments between the two critical points, while the crossings themselves are treated via the zero-mode transfer probabilities. Nevertheless, the manuscript does not supply explicit error estimates or direct numerical benchmarks comparing the WKB phase to exact time evolution. In the revised version we will add (i) a quantitative estimate of non-adiabatic corrections based on the Landau-Zener formula for the chosen ramp speeds and (ii) direct numerical comparisons of the interference patterns obtained from WKB versus exact diagonalization for representative paths. revision: yes

  2. Referee: [Detection via boundary particle number] Section describing the boundary-particle-number detection: the claim that the zero-mode transfer probability is captured by the deviation of the boundary particle number from its initial fractional value relies on the blending of bulk modes, but the manuscript does not quantify how this deviation isolates the ICDZM contribution from other critical or non-critical bulk effects, nor does it compare the predicted deviation magnitude against the known anomalous defect production in the non-closed case.

    Authors: We concur that additional quantification is needed to demonstrate isolation of the ICDZM signal. The current text shows that the boundary deviation encodes the zero-mode transfer probability but does not separate the ICDZM oscillatory component from other bulk contributions or benchmark it against the open-path anomalous production. In the revision we will include (i) a decomposition of the boundary deviation into ICDZM and residual bulk terms for several ramp speeds and (ii) a direct magnitude comparison between the closed-path deviation and the known anomalous defect density reported for non-closed quenches. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained against external benchmarks

full rationale

The abstract presents numerical observation of ICDZM patterns (vanishing or period-doubling) for closed quench paths linking topological phases, followed by an explanatory appeal to standard WKB phase accumulation along those paths. No equations appear, no parameters are fitted then relabeled as predictions, and no self-citations or uniqueness theorems are invoked. The WKB step is an independent analytic tool whose validity is an external question of approximation quality, not a definitional reduction of the observed patterns to themselves. The paper therefore remains self-contained; any concern about non-adiabatic corrections at gap-closing points is a correctness issue, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only. The central claim rests on the validity of the generalized Creutz ladder Hamiltonian, the existence of zero modes at critical points, and the applicability of WKB to the quench dynamics. No free parameters, axioms, or invented entities are explicitly listed.

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