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arxiv: 2607.01344 · v1 · pith:SI5KPGZRnew · submitted 2026-07-01 · ❄️ cond-mat.str-el

Quantum Tunneling-induced Hybridization and Coherent Dynamics of Jackiw-Rebbi Zero Modes in a Modified Su-Schrieffer-Heeger Chain

Surajit Mandal This is my paper

Pith reviewed 2026-07-03 18:40 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Jackiw-Rebbi zero modesmodified SSH modelquantum tunnelinghybridizationcoherent dynamicstopological bound statesDirac gap closing
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The pith

Quantum tunneling between two Jackiw-Rebbi zero modes in a modified SSH chain lifts their degeneracy and produces coherent oscillations of occupation probability.

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

The paper investigates a modified Su-Schrieffer-Heeger chain that supports Jackiw-Rebbi zero modes at two spatially separated interfaces created by a kink profile. Finite overlap between these modes allows quantum tunneling that splits the zero-energy degeneracy into symmetric and antisymmetric hybridized states. An effective two-level model captures the resulting coherent dynamics, in which the occupation probability oscillates between the two modes with a period set by the hybridization gap. During each cycle the sublattice polarization transfers periodically between the (A,C) and (B,D) sectors. The construction supplies a controllable route to topological state transfer in lattice systems.

Core claim

In the modified SSH model the Dirac-type gap closing at k=±π/4a permits an effective mass that reverses sign at two interfaces under a kink, binding a pair of JR zero modes. Their finite overlap lifts the degeneracy through tunneling, yielding symmetric-antisymmetric hybridized states. The resulting two-level dynamics produces coherent oscillations of the mode occupation probability together with periodic transfer of sublattice polarization between the (A,C) and (B,D) sectors, with the oscillation period fixed by the hybridization gap.

What carries the argument

Jackiw-Rebbi zero modes localized at the two kink interfaces, hybridized by quantum tunneling into an effective two-level system that governs coherent oscillations.

If this is right

  • The hybridization gap sets the oscillation period of the coherent dynamics between the two JR modes.
  • Sublattice polarization transfers back and forth between the (A,C) and (B,D) sectors on the same timescale.
  • The oscillation frequency can be tuned by adjusting the spatial separation of the interfaces.
  • The framework connects JR zero modes, tunneling, and coherent control within modified SSH lattices.

Where Pith is reading between the lines

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

  • The same tunneling-hybridization picture could apply to other one-dimensional topological models that host multiple zero modes at engineered interfaces.
  • Cold-atom or photonic-lattice realizations could directly measure the predicted polarization transfer during the oscillations.
  • Extending the two-mode description to chains with three or more JR modes might enable multi-state quantum-state transfer protocols.

Load-bearing premise

The low-energy Dirac theory around the Dirac gap closing points correctly predicts that the effective mass reverses sign at the two spatially separated interfaces of the kink profile.

What would settle it

Absence of any energy splitting between the zero modes or absence of coherent oscillations in the occupation probability when the two interfaces are brought within tunneling range.

Figures

Figures reproduced from arXiv: 2607.01344 by Surajit Mandal.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The profile for effective Dirac mass, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: (b), which shows the disappearance of ZES for very small and very large values of ∆0. For 0 < ∆0 < √ 2t, two in-gap states are exactly at zero energy and remain localized at the two ends of the chain[29]. This is because the hopping arrangements change at the chain center in such a way that no DW can exist at the chain center within this ∆0 regime, similar to the no mass inversion and results in the non-ex… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a)) and non-existence of JR modes. Case II: For ∆0 > √ 2t, the condition M(x) = 0 give mass inversion at the two interfaces at xL = x0 − x⋆ and xL = x0 +x⋆. Inside the two interfaces xL < x < xR, the condition |∆(x)| < √ 2t giving W(x) = 1. While outside the region, |∆(x)| > √ 2t condition provide W(x) = 0 (look at the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
read the original abstract

We investigate analytically and numerically the tunneling-induced hybridization and coherent dynamics of Jackiw-Rebbi (JR) zero modes in a modified Su-Schrieffer-Heeger (SSH) model. Unlike the conventional SSH model, this modified system possess two bulk gap closing points, namely, the quadratic-type gap closing point at $k=0$ and the Dirac-type gap closing point at $k=\pm\pi/4a$. While the quadratic point does not support a topological domain wall due to the absence of mass inversion, the low-energy Dirac theory around $k=\pm\pi/4a$ predicts an effective mass that changes sign at two spatially separated interfaces under a kink profile, generating a pair of JR bound states localized at those interfaces. We show that finite overlap between the JR zero modes lifts the zero-energy degeneracy through quantum tunneling, producing symmetric-antisymmetric hybridized states analogous to a quantum mechanical double-well system. An effective two-level description reveals coherent oscillations of the occupation probability between the two JR modes, accompanied by periodic transfer of sublattice polarization between the (A,C) and (B,D) sectors. The oscillation period is governed by the hybridization gap, providing a tunable route for controlling topological bound states. Our results establish a unified framework connecting JR zero modes, quantum tunneling, and coherent dynamics in modified SSH systems, offering a promising platform for controllable topological quantum-state transfer in engineered lattice structures.

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

0 major / 3 minor

Summary. The manuscript investigates analytically and numerically the tunneling-induced hybridization of Jackiw-Rebbi zero modes in a modified Su-Schrieffer-Heeger chain that features both a quadratic gap closing at k=0 and Dirac-type closings at k=±π/4a. It argues that a kink profile induces mass sign changes only at the Dirac points, localizing a pair of JR bound states whose finite overlap lifts the zero-energy degeneracy, producing symmetric-antisymmetric hybridized states. An effective two-level model is derived to describe coherent oscillations of occupation probability between the modes together with periodic sublattice polarization transfer between (A,C) and (B,D) sectors, with the oscillation period set by the hybridization gap.

Significance. If the derivations hold, the work supplies a concrete lattice realization connecting JR zero modes, quantum tunneling, and coherent dynamics, with an explicit tunable handle (the hybridization gap) for topological state transfer. The separation of quadratic versus Dirac gap-closing physics and the mapping onto a double-well analogy are potentially useful for engineered topological platforms.

minor comments (3)
  1. [Abstract] Abstract and §2: the lattice constant a appears in the wave-vector locations k=±π/4a without an explicit statement of its value or normalization; adding a sentence defining the unit cell length would improve readability.
  2. [§3] §3 (effective two-level model): the hybridization matrix element is stated to be obtained from overlap integrals, but the explicit functional dependence on the kink width or separation is not summarized in the main text; a compact expression or scaling relation would strengthen the claim of tunability.
  3. [Figures] Figure captions: several panels show time-dependent polarization without indicating the numerical time-step or convergence criterion used in the exact diagonalization; adding this information would aid reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central derivation proceeds from the standard low-energy Dirac Hamiltonian around the Dirac points k=±π/4a, where a kink-induced sign change in the effective mass produces JR zero modes by the usual Jackiw-Rebbi mechanism; the quadratic gap closing at k=0 is explicitly shown to lack mass inversion and thus no topological interface states. Finite overlap between the resulting localized modes is then treated with ordinary degenerate perturbation theory to obtain the hybridization gap and the effective two-level coherent dynamics. No fitted parameters are relabeled as predictions, no load-bearing uniqueness theorem is imported via self-citation, and the analytic steps remain independent of the numerical checks. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted with certainty. The model is described as a 'modified' SSH chain, implying additional hopping or mass terms whose precise functional form and any fitting are unknown.

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Reference graph

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