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arxiv: 2512.15417 · v2 · submitted 2025-12-17 · ❄️ cond-mat.stat-mech

Dynamical Scarring from Scrambling in Two Dimensional Topological Materials

Dominik Szpara , Szczepan G{\l}odzik , Nicholas Sedlmayr This is my paper

Pith reviewed 2026-05-16 21:32 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords dynamical scarringout-of-time ordered correlatorstopological edge modesquantum information scramblingtwo-dimensional topological materialschiral and helical modesbutterfly velocity
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The pith

Topological edge modes in two-dimensional materials create dynamical scars where information propagates without scrambling.

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

The paper studies how information scrambles in two dimensional topological models by looking at out-of-time ordered correlators. In the bulk the spread speed varies with direction because of the lattice. Edge modes lead to dynamical scarring in which a boundary perturbation travels around the edge carried by the modes and stays unscrambled for long times. The scars follow the speed and direction of the edge modes and pass through each other.

Core claim

In two dimensional topological models, chiral or helical edge modes cause dynamical scarring where information from an initial boundary perturbation propagates around the edge without being scrambled over long timescales, with the direction and speed of the scars determined by the velocities of the linearly dispersing edge modes, and these scars do not interact with each other.

What carries the argument

Out-of-time ordered correlators that track the spreading of an initial perturbation, showing both lattice-dependent bulk butterfly velocities and persistent edge scars from topological modes.

If this is right

  • Information remains trapped on the system boundary for extended periods rather than spreading into the bulk.
  • The scars propagate at constant velocities matching those of the edge modes.
  • Multiple scars can coexist and cross paths without interfering.
  • Bulk information spreading acquires a directional bias from the underlying lattice.

Where Pith is reading between the lines

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

  • This mechanism could allow topological edges to preserve quantum information against scrambling for practical timescales.
  • Similar scarring might occur in other protected mode systems such as photonic or acoustic topological insulators.
  • Experimental detection could use time-resolved measurements of correlation functions on material edges.
  • The non-interaction of scars points to an effectively linear dynamics on the boundary despite bulk chaos.

Load-bearing premise

The edge modes continue to disperse linearly and remain non-interacting without scattering or decoherence effects over the long evolution times considered.

What would settle it

A numerical computation of the out-of-time ordered correlator on a finite topological lattice model showing whether the boundary signal decays or spreads into the bulk after a time much longer than the edge traversal time.

Figures

Figures reproduced from arXiv: 2512.15417 by Dominik Szpara, Nicholas Sedlmayr, Szczepan G{\l}odzik.

Figure 1
Figure 1. Figure 1: FIG. 1. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Waterfall plots for the OTOC only on the edge of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The location of the dynamical scar on the boundary, [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The OTOC [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Out-of-time ordered correlators are a probe of how the information of an initial perturbation is effectively scrambled under unitary time evolution, widely used to study quantum chaos. They have also been used to demonstrate that information is trapped in the zero dimensional edge modes of topological insulators and superconductors, and does not become scrambled. Here we study scrambling in two dimensional topological models. In the bulk the butterfly velocity, the speed at which the out-of-time ordered correlator spreads, gains a directional dependence from the underlying lattice. Furthermore when there are chiral or helical edge modes present these cause a form of dynamical scarring. The information about an initial perturbation on the boundary of the system travels around the edge, carried by the edge modes, but is not scrambled over very long time scales. The direction and speed of the scars are given by the velocities of the linearly dispersing edge modes. We further show that these scars do not interact, passing through each other. We back up these results with analytical and numerical calculations on exemplary models.

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. The paper claims that out-of-time-ordered correlators (OTOCs) in two-dimensional topological models exhibit a lattice-induced directional dependence in the bulk butterfly velocity. When chiral or helical edge modes are present, they produce dynamical scarring: an initial boundary perturbation propagates along the edge without scrambling over long timescales, with scar direction and speed set by the linear dispersion of the edge modes. The scars are shown to be non-interacting and pass through each other. These findings are supported by analytical derivations and numerical calculations on exemplary models such as lattice Dirac and BHZ-type Hamiltonians.

Significance. If the central claims hold, the work demonstrates how topological protection suppresses scrambling along edges, yielding persistent, non-interacting information channels. This provides a concrete link between topology and quantum chaos diagnostics, with potential relevance to controlled information propagation in quantum devices. The parameter-free character of the edge-mode velocities and the explicit demonstration of non-interacting scars are notable strengths.

major comments (1)
  1. [Numerical results and discussion of long-time behavior] The finite-time nature of the non-scrambling claim is internally consistent with the gapped bulk and protected edge modes, but the manuscript should explicitly bound the timescale on which higher-order corrections (e.g., weak disorder or interactions) remain negligible; without this, the extrapolation to 'very long time scales' in the abstract risks overstatement.
minor comments (2)
  1. [Methods / Model Hamiltonians] The definition of the OTOC operator and the precise lattice regularization used for the edge-mode velocity should be stated once in the main text before the first numerical figure.
  2. [Figures] Figure captions for the OTOC snapshots should include the system size, time range, and any averaging procedure to allow direct comparison with the analytical edge-mode prediction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment and constructive comment on our manuscript. We address the major comment below and will incorporate the suggested revision.

read point-by-point responses

  1. Referee: [Numerical results and discussion of long-time behavior] The finite-time nature of the non-scrambling claim is internally consistent with the gapped bulk and protected edge modes, but the manuscript should explicitly bound the timescale on which higher-order corrections (e.g., weak disorder or interactions) remain negligible; without this, the extrapolation to 'very long time scales' in the abstract risks overstatement.

    Authors: We agree that an explicit bound strengthens the presentation. In the revised manuscript we will add a paragraph (in the main text near the discussion of edge scars) providing a perturbative estimate: in the ideal gapped models the non-scrambling persists for all times, while for weak perturbations of strength ε ≪ Δ (where Δ is the bulk gap) the protection holds up to times ~ Δ/ε² from Fermi-golden-rule scattering rates. We will also revise the abstract phrasing from 'very long time scales' to 'timescales much longer than the inverse bulk gap, set by the strength of any weak perturbations'. This change is consistent with the existing analytical and numerical results. revision: yes

Circularity Check

0 steps flagged

Derivation is self-contained with no circular steps

full rationale

The paper's central claims follow from direct application of standard OTOC definitions to lattice Dirac and BHZ Hamiltonians whose edge modes are linearly dispersing by construction of the topological bulk gap. Analytical propagation of operator support along the boundary and numerical verification of non-interacting scars are obtained without fitted parameters, self-referential definitions, or load-bearing self-citations; the finite-time non-scrambling is a direct consequence of the protected linear dispersion and bulk suppression, making the derivation independent of its target results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics for unitary evolution and OTOCs, plus the assumption of linearly dispersing edge modes in specific lattice models; no new free parameters or invented entities are introduced beyond conventional topological insulator Hamiltonians.

axioms (2)
  • standard math Unitary time evolution under a time-independent Hamiltonian governs the system dynamics
    Invoked for defining out-of-time-ordered correlators and their spreading.
  • domain assumption Topological edge modes in 2D lattices are chiral or helical and linearly dispersing
    Central to the scarring mechanism described in the abstract.

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