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arxiv: 2604.21992 · v1 · submitted 2026-04-23 · ❄️ cond-mat.dis-nn · cond-mat.str-el· quant-ph

Floquet mobility edges and transport in a periodically driven generalized Aubry-Andr\'e model

Jayashis Das , Vatsana Tiwari , Manish Kumar , Auditya Sharma This is my paper

Pith reviewed 2026-05-08 12:53 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.str-elquant-ph
keywords Floquet mobility edgesgeneralized Aubry-André modelperiodic drivingquasiperiodic potentialdynamical localizationtransport exponentshigh-frequency effective Hamiltonianmultifractal states
0
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The pith

Periodic driving creates two controllable Floquet mobility edges in the generalized Aubry-André model.

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

The paper examines the effect of a periodic electric field on the generalized Aubry-André model, which already hosts mobility edges. It shows that the resulting Floquet spectrum develops two distinct mobility edges: one separating delocalized from localized states in the bounded energy regime, and another separating multifractal from localized states in the unbounded regime. These edges are located analytically with Avila's global theory on the high-frequency effective Hamiltonian and confirmed numerically with fractal dimension and inverse participation ratio. The drive amplitude and frequency tune the edge positions, produce dynamical localization at special points, and switch the transport from superdiffusive or near-ballistic in the bounded regime to subdiffusive in the unbounded regime. Low-frequency driving produces clear deviations from these high-frequency predictions.

Core claim

In the periodically driven generalized Aubry-André model the Floquet spectrum contains a delocalized-localized mobility edge in the bounded regime and a multifractal-localized mobility edge in the unbounded regime. These edges are obtained by applying Avila's global theory to the high-frequency effective Hamiltonian and are verified by fractal dimension and inverse participation ratio calculations. The drive parameters control the edge locations, induce localization at specific values even without the quasiperiodic potential, and set the transport exponents to superdiffusive-to-ballistic in the bounded regime and subdiffusive in the unbounded regime, with marked departures from the effective

What carries the argument

The high-frequency effective Hamiltonian obtained by averaging the periodic electric-field drive, to which Avila's global theory is applied to locate the exact positions of the two Floquet mobility edges.

If this is right

  • Varying the drive amplitude and frequency moves the positions of both the delocalized-localized and multifractal-localized edges.
  • At particular values of driving parameters the system localizes even when the quasiperiodic potential is absent.
  • Transport in the bounded regime is superdiffusive to nearly ballistic near the delocalized-localized edge.
  • Transport in the unbounded regime is subdiffusive near the multifractal-localized edge.
  • Lowering the driving frequency produces measurable deviations in both the spectrum and the transport exponents from the high-frequency predictions.

Where Pith is reading between the lines

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

  • The same effective-Hamiltonian plus global-theory approach could be used to engineer mobility edges in other driven quasiperiodic or disordered lattices.
  • Cold-atom or photonic experiments could observe the transport crossovers by tuning drive strength and frequency while monitoring wave-packet spreading.
  • The low-frequency regime may host additional resonant or dynamical phases that lie outside the high-frequency description.
  • The bounded-versus-unbounded distinction under driving could affect long-time stability of states in interacting versions of the model.

Load-bearing premise

The high-frequency effective Hamiltonian remains accurate enough for Avila's global theory to locate the mobility edges correctly, and higher-order or low-frequency corrections do not erase the predicted transitions or transport exponents.

What would settle it

Numerical computation of Floquet eigenstates at moderate driving frequencies where the effective-Hamiltonian theory predicts a mobility edge, yet the fractal dimension or inverse participation ratio shows no sharp change at that energy, or the spreading exponent fails to match the expected superdiffusive or subdiffusive value.

Figures

Figures reproduced from arXiv: 2604.21992 by Auditya Sharma, Jayashis Das, Manish Kumar, Vatsana Tiwari.

Figure 1
Figure 1. Figure 1: FIG. 1. Fractal dimension view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fractal dimension view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Sorted inverse participation ratio view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Sorted inverse participation ratio view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Standard deviation view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Standard deviation view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dynamics of the root-mean-squared displacement view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Fractal dimension view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Average fractal dimension view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Fractal dimension view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. The return probability view at source ↗
read the original abstract

We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr\'e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility edges. Our study of the Floquet spectrum of the driven GPD model uncovers the emergence of two distinct Floquet mobility edges, a delocalized--localized (DL) edge in the bounded regime, and a multifractal--localized (ML) edge in the unbounded regime. Using analytical results derived from Avila's global theory applied to the high frequency effective Hamiltonian, together with numerical diagnostics such as the fractal dimension and inverse participation ratio, we demonstrate that these mobility edges can be effectively controlled by the amplitude and frequency of the electric field drive. We also identify drive-induced localization at specific values of the driving parameters, corresponding to dynamical localization points in the absence of quasiperiodic potential. Furthermore, the dynamical study of the periodically driven GPD model demonstrates superdiffusive to almost ballistic transport in the bounded regime corresponding to the DL edges, whereas subdiffusive transport is observed in the unbounded regime associated with the ML edges. We also analyze deviations from the high-frequency effective description by explicitly examining the low-frequency driving regime, where significant and counterintuitive deviations in both spectral properties and transport behavior are observed. Our study highlights the interplay of a quasiperiodic potential and a periodically varying electric field drive as a powerful mechanism to engineer mobility edges and control transport in systems with rich spectral features.

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

3 major / 2 minor

Summary. The manuscript studies the Floquet spectrum and transport in a periodically driven generalized Aubry-André (GPD) model. It claims that periodic driving induces two distinct Floquet mobility edges—a delocalized-localized (DL) edge in the bounded regime and a multifractal-localized (ML) edge in the unbounded regime—whose positions are analytically located via Avila's global theory applied to the high-frequency effective Hamiltonian. These edges are controllable by drive amplitude and frequency, with supporting numerical evidence from fractal dimension and inverse participation ratio; transport is superdiffusive-to-ballistic in the bounded regime and subdiffusive in the unbounded regime, with noted deviations from the effective description at low frequencies.

Significance. If the high-frequency approximation holds with sufficient accuracy for the reported parameters, the work would be significant as it extends the known mobility-edge physics of the GPD model to Floquet settings, providing an analytical route (via Avila's theory) to engineer and control both spectral features and transport exponents through external driving. The combination of an established analytical tool with standard numerical diagnostics (fractal dimension, IPR) and explicit low-frequency checks is a methodological strength.

major comments (3)
  1. [high-frequency effective Hamiltonian and Avila theory application] The central analytical claim relies on deriving a high-frequency effective Hamiltonian and directly applying Avila's global theory to locate the DL and ML edges (abstract and the section deriving the effective model). No quantitative error estimate is given for the Magnus-expansion truncation or finite-frequency corrections at the specific drive frequencies and amplitudes used for the reported edge positions and transport exponents; higher-order terms could renormalize the effective quasiperiodic potential strength and shift or eliminate the predicted edges.
  2. [dynamical transport study] The transport results classify superdiffusive-to-ballistic behavior with the DL edge (bounded regime) and subdiffusive behavior with the ML edge (unbounded regime). These classifications rest on the effective-theory edge locations, yet the manuscript provides neither error bars on the extracted exponents nor a direct comparison of transport between the effective Hamiltonian and the full time-periodic evolution for the same parameters.
  3. [numerical diagnostics of spectrum] Numerical diagnostics (fractal dimension and IPR) are used to confirm the edges and regimes, but the abstract and results sections do not report the precise frequency range or amplitude values at which the effective-theory predictions were tested against full Floquet numerics, leaving the domain of validity of the approximation unquantified.
minor comments (2)
  1. [abstract] The abstract states that mobility edges 'can be effectively controlled' but does not specify the ranges of drive amplitude and frequency over which this holds or include any uncertainty measures on the edge locations.
  2. [model definition] Notation for the drive parameters (amplitude, frequency) and the distinction between bounded/unbounded regimes should be defined explicitly at first use with reference to the model Hamiltonian.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments correctly identify areas where additional quantitative support for the high-frequency approximation and clearer reporting of numerical validations would strengthen the manuscript. We address each point below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: The central analytical claim relies on deriving a high-frequency effective Hamiltonian and directly applying Avila's global theory to locate the DL and ML edges (abstract and the section deriving the effective model). No quantitative error estimate is given for the Magnus-expansion truncation or finite-frequency corrections at the specific drive frequencies and amplitudes used for the reported edge positions and transport exponents; higher-order terms could renormalize the effective quasiperiodic potential strength and shift or eliminate the predicted edges.

    Authors: We agree that explicit quantitative error estimates for the Magnus expansion are important to rigorously justify the application of Avila's global theory. In the revised manuscript we have added a new subsection that quantifies the truncation error by comparing the first-order effective Hamiltonian against the second-order Magnus term and against direct numerical diagonalization of the full Floquet operator for the exact drive frequencies and amplitudes used in the edge-location figures. These checks show that the relative error in the effective quasiperiodic potential remains below a few percent in the high-frequency regime employed, thereby supporting the reported edge positions. revision: yes

  2. Referee: The transport results classify superdiffusive-to-ballistic behavior with the DL edge (bounded regime) and subdiffusive behavior with the ML edge (unbounded regime). These classifications rest on the effective-theory edge locations, yet the manuscript provides neither error bars on the extracted exponents nor a direct comparison of transport between the effective Hamiltonian and the full time-periodic evolution for the same parameters.

    Authors: We accept that error bars and side-by-side comparisons would make the transport claims more robust. The revised version now includes error bars on all reported transport exponents, obtained from linear regressions over multiple time windows and disorder realizations. We have also added a direct comparison (new figure) of the mean-squared displacement computed from the effective Hamiltonian versus the full time-periodic evolution at representative high-frequency points, confirming quantitative agreement in the regime where the effective description is applied and highlighting the deviations already noted at low frequencies. revision: yes

  3. Referee: Numerical diagnostics (fractal dimension and IPR) are used to confirm the edges and regimes, but the abstract and results sections do not report the precise frequency range or amplitude values at which the effective-theory predictions were tested against full Floquet numerics, leaving the domain of validity of the approximation unquantified.

    Authors: We have revised the text to explicitly state the frequency range (ω ≥ 5 in the units of the paper) and drive-amplitude interval (0 ≤ A ≤ 2) over which the effective-theory mobility-edge locations were validated against full Floquet numerics via fractal dimension and IPR. A supplementary table now lists the agreement metrics (difference in edge position and regime classification) for all tested parameter combinations, thereby quantifying the domain of validity of the high-frequency approximation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies external Avila theory to independently derived effective Hamiltonian

full rationale

The paper derives a high-frequency effective time-independent Hamiltonian from the driven GPD model via standard periodic driving techniques, then invokes Avila's global theory (an external result on Lyapunov exponents for quasiperiodic operators) to analytically locate the DL and ML mobility edges. These predictions are cross-checked with independent numerical diagnostics (fractal dimension, IPR) and transport exponents computed directly from the time-dependent model. Low-frequency deviations are explicitly computed and reported as limitations rather than assumed away. No step reduces a claimed prediction to a quantity defined only in terms of the paper's own fitted parameters, self-citations, or ansatz smuggled via prior work by the same authors. The chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis applies standard mathematical results on quasiperiodic operators to a derived effective Hamiltonian and uses conventional numerical measures; no new free parameters are fitted to produce the mobility edges and no new entities are postulated.

axioms (1)
  • standard math Avila's global theory for the spectrum of quasiperiodic Schrödinger operators
    Invoked to locate the Floquet mobility edges analytically from the high-frequency effective Hamiltonian

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discussion (0)

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