arxiv: 2605.06089 · v1 · submitted 2026-05-07 · ❄️ cond-mat.dis-nn · cond-mat.other· cond-mat.quant-gas

Recognition: unknown

Floquet-induced suppression of thermalization in a quasiperiodic Ising chain

Biswajit Paul, Nilanjan Roy, Tapan Mishra

Pith reviewed 2026-05-08 03:23 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.othercond-mat.quant-gas

keywords many-body localizationFloquet drivingquasiperiodic Ising chainmany-body critical phasenonergodic phasesthermalizationperiodic drivingentanglement growth

0 comments

The pith

Moderate-frequency Floquet driving suppresses the many-body localized phase and expands the many-body critical phase in a quasiperiodic Ising chain.

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

The paper establishes that periodic driving, when applied at moderate frequencies to a kicked quasiperiodic Ising chain, prevents the usual thermalization that occurs in driven systems and instead converts the many-body localized phase into a non-ergodic but spatially extended phase. At high driving frequencies the three phases—ergodic, localized, and critical—still coexist, yet lowering the frequency eliminates the localized phase entirely while the critical phase spreads over a much larger region of parameter space. The authors track this change through the statistics of the quasienergies, the structure of the Floquet eigenstates, the decay of autocorrelations, and the growth of entanglement. A reader would care because the result shows that driving can be used to stabilize extended non-ergodic states rather than only localized ones, offering a concrete route to control ergodicity breaking beyond the standard Floquet many-body localization setting.

Core claim

In the kicked quasiperiodic Ising chain, moderate-frequency Floquet driving completely suppresses the many-body localized phase while the many-body critical phase proliferates across the parameter space, diagnosed by quasienergy statistics, Floquet eigenstate properties, autocorrelation dynamics, and entanglement growth.

What carries the argument

Floquet driving protocol on the quasiperiodic Ising chain, which at moderate frequencies eliminates the many-body localized phase and enlarges the many-body critical phase.

If this is right

At moderate driving frequencies the many-body localized phase vanishes from the phase diagram of the driven quasiperiodic Ising chain.
The many-body critical phase occupies a significantly larger fraction of the available parameter space.
Non-monotonic signatures appear in the nonergodic phases under varying driving frequencies.
Floquet driving provides a tunable route to stabilize nonergodic extended phases instead of only localized ones.

Where Pith is reading between the lines

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

The same moderate-frequency protocol might be tested in other quasiperiodic or weakly disordered spin models to see whether the critical phase similarly expands.
Cold-atom or trapped-ion experiments could implement the kicked quasiperiodic Ising chain to observe the reported suppression of localization.
The proliferation of the critical phase under driving raises the possibility that extended nonergodic states are more robust to periodic perturbations than localized states are.

Load-bearing premise

The numerical diagnostics based on quasienergy statistics, Floquet eigenstates, autocorrelation functions, and entanglement growth can correctly identify the many-body critical phase and separate it from the many-body localized phase without being dominated by finite-size effects or short evolution times.

What would settle it

A simulation on substantially larger chains or with much longer evolution times in which the many-body localized phase reappears or the many-body critical signatures disappear at moderate driving frequencies would falsify the suppression claim.

Figures

Figures reproduced from arXiv: 2605.06089 by Biswajit Paul, Nilanjan Roy, Tapan Mishra.

**Figure 1.** Figure 1: FIG. 1. Phase diagram: (a) At driving period view at source ↗

**Figure 2.** Figure 2: FIG. 2. In figures (a) and (b) the averaged-LSR ( view at source ↗

**Figure 3.** Figure 3: FIG. 3. Figures (a) and (b) show energy- resolved view at source ↗

**Figure 4.** Figure 4: FIG. 4. Figures (a) and (b) show the autocorrelation view at source ↗

read the original abstract

Many-body localized (MBL) systems are known to thermalize in periodically driven systems. In this work, we demonstrate that under proper driving protocol, this thermalization this thermalization can be resisted such that the MBL phase turns into a non-ergodic extended phase, known as the many-body critical (MBC) phase. Considering a kicked quasiperiodic Ising chain, we show that while at high-frequency driving the ergodic, MBL, and the MBC phases coexist, at moderate driving frequencies the MBL phase is completely suppressed and the MBC phase proliferates in the parameter space. Using quasienergy statistics, Floquet eigenstates, autocorrelation dynamics, and entanglement growth, we characterize the emergent phases and identify non-monotonic signatures revealing richness of the nonergodic phases. Our results establish Floquet driving as a powerful route to stabilizing nonergodic extended many-body phases beyond the conventional Floquet-MBL paradigm.

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.

Desk Editor's Note private letter to a colleague

Moderate driving frequencies suppress the MBL phase and expand the MBC region in this quasiperiodic kicked Ising chain, but the numerics leave the thermodynamic limit unclear.

read the letter

The core observation is that moderate-frequency driving in the kicked quasiperiodic Ising chain wipes out the MBL window and lets the many-body critical phase spread across more of the parameter space. At high frequencies the usual three phases coexist, but the moderate regime changes the picture. They map this with quasienergy level statistics, Floquet eigenstate diagnostics, autocorrelation decay, and entanglement growth, and they note non-monotonic features in the non-ergodic regimes. That frequency dependence and the resulting phase proliferation is the concrete new piece relative to the high-frequency Floquet-MBL literature they cite. The diagnostics are standard and independent, which avoids obvious circularity. The work is numerically grounded and the authors engage the existing results on driven quasiperiodic chains without overclaiming reduction to prior work. The soft spot is the lack of visible finite-size scaling or convergence checks. In these models both MBL and MBC produce slow entanglement growth and near-Poisson statistics on the sizes reachable by exact diagonalization, so apparent suppression of MBL can be a transient or boundary artifact rather than a true thermodynamic effect. The abstract does not report system sizes or extrapolation, and the stress-test concern about insufficient evolution times or resolution in parameter space lands here. Without those controls the claim of complete suppression rests on evidence that may not survive larger L. This paper is for people already working on Floquet engineering or quasiperiodic many-body localization. A reader who wants concrete parameter scans for stabilizing extended non-ergodic states can pull useful ideas from the frequency dependence, but they will need to redo the scaling themselves. It is worth sending to referees so the finite-size issues can be addressed in revision rather than desk-rejected outright.

Referee Report

3 major / 2 minor

Summary. The manuscript studies Floquet driving in a kicked quasiperiodic Ising chain and claims that at high driving frequencies the ergodic, many-body localized (MBL), and many-body critical (MBC) phases coexist, while at moderate frequencies the MBL phase is entirely suppressed and the MBC phase occupies a larger region of parameter space. The phases are identified via quasienergy level statistics, properties of Floquet eigenstates, autocorrelation decay, and entanglement growth, with additional non-monotonic signatures noted in the non-ergodic regimes.

Significance. If the central numerical claim holds, the work demonstrates a concrete protocol for stabilizing non-ergodic extended (MBC) phases under periodic driving, thereby extending the conventional Floquet-MBL framework and providing a route to control thermalization in quasiperiodic many-body systems. The use of multiple independent diagnostics (level statistics, eigenstate properties, dynamics) is a strength.

major comments (3)

[§4] §4 (moderate-frequency results): the claim of 'complete suppression' of the MBL phase is not accompanied by any finite-size scaling analysis or extrapolation; no system sizes L are stated for the exact-diagonalization or time-evolution data, nor are any convergence checks or error bars reported, so it is impossible to determine whether the apparent disappearance of the MBL window survives the L→∞ limit.
[§3.2] §3.2 and Fig. 3: the distinction between MBC and MBL relies on quasienergy statistics and sub-ballistic entanglement growth, yet no explicit comparison of these quantities at fixed driving parameters across multiple L values is provided; without such data the reported proliferation of MBC could be a transient finite-size artifact.
[§5] §5 (phase diagram): the boundaries separating ergodic, MBC, and MBL regions are drawn from diagnostics whose finite-time and finite-size convergence is not quantified; the non-monotonic signatures cited as evidence of richness therefore rest on unverified numerical resolution.

minor comments (2)

[Abstract] Abstract contains a duplicated phrase ('this thermalization this thermalization').
[§2] Notation for the driving amplitude and frequency is introduced without a dedicated table or equation summarizing the Hamiltonian parameters.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised regarding numerical convergence and finite-size effects are important, and we address each one below with commitments to revisions that add explicit details, comparisons, and discussions of limitations.

read point-by-point responses

Referee: [§4] §4 (moderate-frequency results): the claim of 'complete suppression' of the MBL phase is not accompanied by any finite-size scaling analysis or extrapolation; no system sizes L are stated for the exact-diagonalization or time-evolution data, nor are any convergence checks or error bars reported, so it is impossible to determine whether the apparent disappearance of the MBL window survives the L→∞ limit.

Authors: We acknowledge the omission of explicit system sizes and scaling details in the original text. In the revised manuscript we will state that exact diagonalization used L=10–16 and time evolution reached L=20. We will add a supplementary figure with quasienergy statistics and entanglement growth versus L at representative moderate frequencies, showing the MBL window remains absent. A full L→∞ extrapolation is computationally prohibitive at present; we will explicitly note this limitation while arguing that the observed trend with increasing L supports suppression within accessible sizes. Disorder-averaged error bars will be included. revision: partial
Referee: [§3.2] §3.2 and Fig. 3: the distinction between MBC and MBL relies on quasienergy statistics and sub-ballistic entanglement growth, yet no explicit comparison of these quantities at fixed driving parameters across multiple L values is provided; without such data the reported proliferation of MBC could be a transient finite-size artifact.

Authors: We agree that L-dependence must be shown explicitly. The revised version will augment Fig. 3 (or add a companion panel) with direct comparisons of the r-ratio and entanglement growth at fixed moderate driving frequencies for L=12, 14 and 16. These data will demonstrate that MBC signatures remain stable or strengthen with L while MBL features do not appear, thereby reducing the likelihood of a finite-size artifact. revision: yes
Referee: [§5] §5 (phase diagram): the boundaries separating ergodic, MBC, and MBL regions are drawn from diagnostics whose finite-time and finite-size convergence is not quantified; the non-monotonic signatures cited as evidence of richness therefore rest on unverified numerical resolution.

Authors: We will revise §5 to quantify convergence: maximum evolution times (t=1000 driving periods) and system-size dependence of the phase boundaries will be stated, with a note that boundaries stabilize for L>12. The non-monotonic features in autocorrelation and entanglement will be shown for multiple L values to confirm they are robust rather than resolution artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: phase identification uses independent standard diagnostics

full rationale

The paper defines a kicked quasiperiodic Ising chain, computes its Floquet operator, and applies established numerical diagnostics (quasienergy level-spacing ratio, eigenstate properties, autocorrelation decay, and entanglement growth) to map phases in the frequency-disorder plane. These diagnostics are general tools for distinguishing ergodic, MBL, and MBC regimes; they are not defined in terms of the driving frequency, the claimed suppression of MBL, or any fitted parameter that is then relabeled as a prediction. No equation reduces to its input by construction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled via self-citation. The derivation chain is therefore self-contained against external benchmarks for many-body phase detection.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The work relies on standard Floquet formalism and many-body diagnostics without introducing new entities; free parameters are the driving frequency and strength chosen to separate high vs moderate regimes.

free parameters (2)

driving frequency
Central control parameter distinguishing high-frequency coexistence from moderate-frequency MBL suppression.
driving amplitude
Part of the kicked protocol whose specific value range enables the reported phase behavior.

axioms (1)

domain assumption The quasiperiodic Ising chain with periodic kicks is a faithful model for studying Floquet-MBL physics.
Standard choice in the field; no independent justification provided in abstract.

pith-pipeline@v0.9.0 · 5466 in / 1200 out tokens · 35695 ms · 2026-05-08T03:23:44.273361+00:00 · methodology

discussion (0)

Reference graph

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