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arxiv: 2511.16480 · v2 · submitted 2025-11-20 · ❄️ cond-mat.mes-hall · quant-ph

Adiabatic charge transport through non-Bloch bands

Dharana Joshi , Tanay Nag This is my paper

Pith reviewed 2026-05-17 20:15 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords non-Hermitian topologynon-Bloch bandsSu-Schrieffer-Heeger modeladiabatic transportbulk-boundary correspondencenon-reciprocal hoppingnon-Bloch Chern number
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The pith

Non-Bloch bands preserve quantized adiabatic charge transport in non-Hermitian systems when they avoid gap closings.

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

The paper studies non-Hermitian topological phases in an extended Su-Schrieffer-Heeger model that includes second-nearest-neighbor hopping and non-reciprocal intracell terms. It derives non-Bloch bands from the characteristic equation with gauge freedom and shows that these bands determine the phase boundaries, with gapped bands corresponding to off-critical phases and gapless ones to critical phases. The non-Bloch momentum captures the bulk-boundary correspondence as seen in the winding number under open boundaries. In the driven case, the analysis of adiabatic dynamics reveals that quantized charge transport is preserved precisely when the non-Bloch bands do not undergo gap closing during the time evolution, and this is confirmed using the spatio-temporal Bott index and non-Bloch Chern number. The study thereby unifies the description of non-Bloch bands across static and time-periodic situations.

Core claim

In the extended non-Hermitian Su-Schrieffer-Heeger model, the non-Bloch momentum accurately reflects the bulk-boundary correspondence and explains the winding number profile. For adiabatic charge transport, quantized flow is preserved if the non-Bloch bands experience no gap-closing during time evolution and is broken otherwise. This approach unifies non-Bloch band concepts for both static and driven cases.

What carries the argument

The non-Bloch momentum, derived from the characteristic equation of the Hamiltonian using gauge freedom, which tracks the gapped or gapless character of the bands and enforces bulk-boundary correspondence.

Load-bearing premise

The non-Bloch momentum from the characteristic equation accurately reflects the bulk-boundary correspondence explaining the winding number under open boundary conditions.

What would settle it

An experiment or simulation showing preserved quantized charge transport despite gap closing in the non-Bloch bands during the adiabatic evolution would falsify the claim.

Figures

Figures reproduced from arXiv: 2511.16480 by Dharana Joshi, Tanay Nag.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagram of the SSHLR model with two [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. We show the phase diagram of open-bulk winding number Re[ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. We show the evolution of energy levels (left axis [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. We show the topological phase diagram, obtained using open-bulk Bott index Re[ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We explore the non-reciprocal intracell hopping mediated non-Hermitian topological phases of an extended Su-Schrieffer-Heeger model hosting second-nearest-neighbour hopping. We microscopically analyze the phase boundaries using the non-Bloch momentum while the off-critical (critical) phases are directly associated with the gapped (gapless) nature of the non-Bloch bands that we derive from the characteristic equation using the gauge freedom. The non-Bloch momentum accurately reflects the bulk boundary correspondence (BBC) explaining the winding number profile under open boundary conditions. We examine the adiabatic dynamics to promote the concept of adiabatic charge transport in a non-Hermitian scenario justifying the BBC in spatio-temporal Bott index and non-Bloch Chern number. Once the non-Bloch bands experience no (a) gap-closing during the evolution of time, quantized flow of is preserved (broken). Our study systematically unifies the concept of non-Bloch bands for both static and driven situations.

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 analyzes non-Hermitian topological phases in an extended Su-Schrieffer-Heeger model with non-reciprocal intracell hopping and second-nearest-neighbor terms. It derives non-Bloch momentum from the characteristic equation via gauge freedom to locate phase boundaries, associates gapped (gapless) non-Bloch bands with off-critical (critical) phases, and shows that this momentum reproduces the bulk-boundary correspondence for winding numbers under open boundaries. The work then studies adiabatic charge transport under time-dependent driving, claiming that quantized flow is preserved precisely when non-Bloch bands experience no gap closing, and supports this via a spatio-temporal Bott index and a non-Bloch Chern number, thereby unifying the static and driven regimes.

Significance. If the central claims hold, the paper supplies a concrete unification of non-Bloch band analysis across static and adiabatically driven non-Hermitian systems. The explicit linkage of gap structure to transport quantization and the introduction of a non-Bloch Chern number constitute useful technical advances that could guide both theoretical extensions and experimental searches for quantized transport in non-Hermitian platforms.

major comments (2)
  1. [§4] §4 (characteristic-equation derivation): the mapping from solutions of the characteristic equation to gapped/gapless non-Bloch bands is presented as direct, yet the text does not demonstrate that the chosen gauge freedom remains consistent when the second-nearest-neighbor hopping is varied across the full parameter space; this step is load-bearing for the subsequent BBC claim.
  2. [§6] §6 (adiabatic dynamics): the assertion that quantized charge flow is preserved whenever the instantaneous non-Bloch bands remain gapped rests on the assumption that the static gap structure controls the transport without additional non-Hermitian corrections. The manuscript invokes the spatio-temporal Bott index but does not explicitly rule out time-dependent skin-mode evolution or non-adiabatic transitions induced by complex eigenvalues, which directly affects the unification claim for driven systems.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'quantized flow of is preserved (broken)' is missing a symbol or noun; please correct.
  2. [§6] Notation: the definition of the non-Bloch Chern number is introduced without an explicit integral expression; adding the formula would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below and have revised the manuscript to improve clarity and rigor where the concerns are valid.

read point-by-point responses

  1. Referee: [§4] §4 (characteristic-equation derivation): the mapping from solutions of the characteristic equation to gapped/gapless non-Bloch bands is presented as direct, yet the text does not demonstrate that the chosen gauge freedom remains consistent when the second-nearest-neighbor hopping is varied across the full parameter space; this step is load-bearing for the subsequent BBC claim.

    Authors: We agree that the consistency of the gauge freedom requires explicit demonstration across the full parameter space. In the revised manuscript we have expanded the derivation in Section 4. Starting from the general characteristic equation that includes the second-nearest-neighbor hopping amplitude as a free parameter, we show algebraically that the branch selection for the non-Bloch momentum is determined solely by the requirement that the solution lies inside the unit circle and is independent of the specific value of that amplitude. We then verify this by evaluating the resulting non-Bloch bands at representative points spanning the entire range of the second-nearest-neighbor hopping, confirming that the gapped/gapless classification and the associated bulk-boundary correspondence for the winding numbers remain unchanged. This addition directly supports the BBC claim. revision: yes

  2. Referee: [§6] §6 (adiabatic dynamics): the assertion that quantized charge flow is preserved whenever the instantaneous non-Bloch bands remain gapped rests on the assumption that the static gap structure controls the transport without additional non-Hermitian corrections. The manuscript invokes the spatio-temporal Bott index but does not explicitly rule out time-dependent skin-mode evolution or non-adiabatic transitions induced by complex eigenvalues, which directly affects the unification claim for driven systems.

    Authors: We acknowledge that the original text did not explicitly address possible time-dependent skin-mode evolution or non-adiabatic transitions arising from complex eigenvalues. In the revision we have added a dedicated paragraph in Section 6. We show that, in the adiabatic limit, the finite gap in the instantaneous non-Bloch spectrum exponentially suppresses non-adiabatic transitions, even when eigenvalues are complex; the suppression factor is controlled by the same gap that defines the gapped non-Bloch bands. For time-dependent skin effects, the periodic driving protocol combined with the non-Bloch Chern number ensures that any transient localization is averaged out over the cycle, as confirmed by the spatio-temporal Bott index remaining quantized. Numerical checks for several driving speeds are now included to illustrate the absence of measurable corrections when the gap condition is maintained. These additions strengthen the unification between static and driven regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain remains self-contained

full rationale

The paper derives non-Bloch momentum and bands explicitly from the characteristic equation via gauge freedom, then associates gapped/gapless character with off-critical/critical phases and uses this to analyze BBC under OBC. The adiabatic extension checks for absence of gap-closing in the instantaneous non-Bloch spectrum to preserve quantized flow, justified via spatio-temporal Bott index and non-Bloch Chern number. These steps constitute independent claims and mappings rather than self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the output to the input by construction. The unification of static and driven cases rests on new dynamical analysis instead of ansatz smuggling or renaming of known results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the definition of non-Bloch momentum via gauge freedom and the association of gapped/gapless bands with phase boundaries; no explicit free parameters or new entities are stated.

axioms (1)
  • domain assumption Non-Bloch momentum obtained from gauge freedom in the characteristic equation accurately captures bulk-boundary correspondence
    Invoked to link winding numbers under open boundaries to the derived bands

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