arxiv: 2604.20419 · v1 · submitted 2026-04-22 · ❄️ cond-mat.stat-mech · quant-ph

Recognition: unknown

Quantum many-body scars leading to time-translation symmetry breaking in kicked interacting spin models

\'Angel L. Corps , Armando Rela\~no , Angelo Russomanno

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:32 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph

keywords quantum many-body scarsFloquet time-translation symmetry breakingperiod doublingkicked Ising modelweak ergodicity breakinglong-range interactionsspin chains

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The pith

Period-doubling oscillations in a kicked long-range Ising model arise from a minority of Floquet states that break time-translation symmetry.

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

The paper investigates how a time-periodically kicked Ising spin chain with long-range interactions can exhibit persistent period-doubling dynamics. For initial states like those with domain walls or tilted spins, the magnetization shows oscillations with twice the driving period. This behavior occurs because the initial state overlaps with specific Floquet eigenstates organized in doublets that display π-spectral pairing and long-range order in magnetization. These symmetry-breaking states represent a form of quantum many-body scars, while the majority of the spectrum remains thermal, leading to weak ergodicity breaking. The exponential growth in the number of such scarred states with system size explains why period doubling appears for many different starting points.

Core claim

When period doubling is observed, the initial state overlaps with Floquet states showing time-translation symmetry breaking. These states form doublets with π-spectral pairing, highlighted by a π-spectral gap, and exhibit long-range order via the eigenvalues of the magnetization operator. Finite-size scaling of the π-shifted gap and magnetization eigenvalues indicates that the period-doubling oscillations persist for larger system sizes and last a time exponential in the system size. Although only a minority of Floquet states display this symmetry breaking, their number is exponential in system size, accounting for the effect across various initial conditions.

What carries the argument

Floquet eigenstate doublets with π-spectral pairing and magnetization long-range order, which carry the time-translation symmetry breaking responsible for period doubling.

If this is right

Period-doubling oscillations can persist exponentially long in system size for appropriate initial states.
The symmetry-breaking states are a minority but exponentially numerous, enabling the phenomenon from many starting configurations.
Most Floquet states are thermal, resulting in weak ergodicity breaking akin to quantum scars.
Initial states with domain walls or tilted spins both exhibit the period-doubling behavior.

Where Pith is reading between the lines

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

Similar scar-induced symmetry breaking might appear in other periodically driven interacting spin models beyond long-range Ising.
The mechanism could be tested by preparing specific initial states in quantum simulators and measuring the duration of oscillations.
Connecting this to other forms of Floquet time crystals might reveal broader classes of non-ergodic driven systems.

Load-bearing premise

The finite-size scaling of the π-spectral gap and magnetization eigenvalues remains stable as system size grows, implying the oscillations do not decay faster than exponentially.

What would settle it

Numerical simulations on larger system sizes showing the π-spectral gap closing to zero or the magnetization eigenvalues becoming size-independent in a way that prevents long-time period doubling.

Figures

Figures reproduced from arXiv: 2604.20419 by \'Angel L. Corps, Angelo Russomanno, Armando Rela\~no.

**Figure 2.** Figure 2: Mode of the coarse-grained normalized-eigenvalue distribution for the two [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: Average level spacing ratio, 〈r〉, versus α. Numerical parameters for panel (a): J = 1, hx = 0.1, hz = 0.2, ε = 0, N = 19. Numerical parameters for panel (b): J = 1, hx = 0.25, hz = 0.0, ε = 0.1, N = 19. The COE and Poisson theoretical values are plotted with red and green horizontal lines. For (b), the Hamiltonian commutes with the parity operator Eq. (A.3); therefore, the ratio reported here is the averag… view at source ↗

**Figure 4.** Figure 4: Scatter plots of the Floquet doublets with half-chain entanglement en [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: Logarithm of the number of long-range ordered Floquet eigenstates ver [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: (a)-(b) Scatter plots where each yellow point corresponds to a Floquet [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 7.** Figure 7: 〈log10 ∆π 〉 [see Eq. (13)] versus N for the two cases considered in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: Mode of the coarse-grained normalized-eigenvalue distribution for the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

read the original abstract

We study an Ising model with long-range interactions undergoing a time-periodic kicking. For different initial states we observe persistent period doubling. When there is period doubling we find that the initial state has relevant overlap with Floquet states showing time-translation symmetry breaking, organized in doublets displaying $\pi$-spectral pairing (as highlighted by the $\pi$-spectral gap) and long-range order (as shown by the eigenvalues of the magnetization in the doublet). We observe period doubling for initial states with domain walls and tilted spins, and for the latter ones a finite-size scaling of the relevant $\pi$-shifted gap and magnetization eigenvalues suggests period-doubling oscillations persisting for larger system sizes and lasting a time exponential in the system size. We find that just a minority of Floquet states displays time-translation symmetry breaking while the rest is thermal, a weak-ergodicity breaking situation typical of systems with quantum scars. Although the time-translation symmetry breaking eigenstates are the minority, their number is exponential in the system size and this motivates the period doubling observed for many different initial states.

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

The paper gives numerical evidence for scar-driven period doubling in a kicked long-range Ising model, but the exponential lifetime claim rests on finite-size scaling whose robustness is not yet clear from the abstract.

read the letter

The main point is that the authors see persistent period-2 oscillations in the magnetization for several initial states in this periodically kicked long-range Ising chain, and they trace it to a subset of Floquet eigenstates that form π-paired doublets carrying long-range order. Only a minority of states show the time-translation symmetry breaking, yet their number grows exponentially with size, which accounts for the effect appearing across many starting conditions. That is a clean illustration of weak ergodicity breaking via scars in a driven setting. What is new here is the specific combination of long-range interactions, the kicking protocol, and the check that the phenomenon holds for both domain-wall and tilted-spin preparations, plus the attempt to quantify the lifetime via scaling of the π-gap and magnetization eigenvalues. The work does a reasonable job linking the spectral features directly to the observed dynamics without obvious circularity. The soft spot is the extrapolation itself. The abstract states that the finite-size trends suggest the oscillations persist exponentially long, but if the gap closes only polynomially or if sub-leading corrections cause saturation, the thermodynamic-limit claim would not stand. Without the actual plots, system sizes, or explicit checks against alternative scalings, it is hard to judge how solid that step is. The rest of the numerics look standard. This is for people working on quantum scars, Floquet systems, and ergodicity breaking. A reader interested in driven quantum matter would get a concrete example and the scaling attempt. I would send it to peer review; the core observation is worth referee time even if the lifetime argument needs tightening.

Referee Report

1 major / 1 minor

Summary. The manuscript examines a long-range interacting Ising model subject to periodic kicking and reports the observation of persistent period-doubling dynamics in several classes of initial states. These dynamics are linked to the initial state's overlap with a subset of Floquet eigenstates that exhibit time-translation symmetry breaking, organized into π-paired doublets characterized by a π-spectral gap and long-range magnetic order. The authors note that while only a minority of Floquet states display this behavior, their number grows exponentially with system size, consistent with quantum many-body scars and weak ergodicity breaking. For initial states with tilted spins, finite-size scaling of the π-gap and magnetization eigenvalues is invoked to argue that the period-doubling persists for times exponential in system size.

Significance. If the reported exponential persistence of the period-doubling holds in the thermodynamic limit, the work would establish a mechanism by which quantum scars can produce long-lived time-translation symmetry breaking in driven spin systems. The exponential scaling of the number of scar states would explain why the effect is observable for a wide range of initial conditions, providing a new example of weak ergodicity breaking in Floquet settings with potential implications for understanding non-ergodic dynamics in periodically driven many-body systems.

major comments (1)

[finite-size scaling discussion for tilted spins] The finite-size scaling analysis of the π-shifted gap and magnetization eigenvalues (as described for the tilted-spin initial states): the statement that this scaling 'suggests' period-doubling oscillations persisting for larger system sizes and lasting a time exponential in the system size is load-bearing for the headline claim of persistent TTSB. No quantitative details are supplied on the system sizes studied, the functional form assumed for the extrapolation, error bars, goodness-of-fit metrics, or explicit checks ruling out polynomial or saturating alternatives; without these the thermodynamic-limit behavior remains unverified.

minor comments (1)

[abstract and results] The abstract and main text use the term 'relevant overlap' with the TTSB doublets without stating a quantitative threshold or overlap measure; specifying this criterion would aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting the importance of rigorous finite-size scaling to support the claim of persistent time-translation symmetry breaking. We address the major comment below and will revise the manuscript to incorporate additional quantitative details as requested.

read point-by-point responses

Referee: The finite-size scaling analysis of the π-shifted gap and magnetization eigenvalues (as described for the tilted-spin initial states): the statement that this scaling 'suggests' period-doubling oscillations persisting for larger system sizes and lasting a time exponential in the system size is load-bearing for the headline claim of persistent TTSB. No quantitative details are supplied on the system sizes studied, the functional form assumed for the extrapolation, error bars, goodness-of-fit metrics, or explicit checks ruling out polynomial or saturating alternatives; without these the thermodynamic-limit behavior remains unverified.

Authors: We agree that the finite-size scaling for tilted-spin initial states is central to the claim of exponentially long-lived period-doubling and that the current phrasing relies on an implicit extrapolation. The manuscript does not currently include the requested quantitative details. In the revised version we will expand this section to specify the system sizes used (up to the largest N accessible in our exact diagonalization), the functional form fitted to the π-gap and magnetization eigenvalues (typically an exponential decay with N), the fitting procedure with associated error bars, goodness-of-fit metrics, and explicit comparisons showing that polynomial or saturating forms are inconsistent with the data. These additions will make the evidence for thermodynamic-limit persistence transparent and address the concern directly. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on direct Floquet numerics and finite-size observations

full rationale

The paper reports numerical observations of period-doubling dynamics, π-spectral pairing in Floquet doublets, and magnetization eigenvalues obtained from exact diagonalization of the kicked Ising model for finite chains. The finite-size scaling of the π-gap and order parameters is presented as suggestive evidence for exponential lifetimes rather than an analytical derivation or fitted prediction. No equations reduce a claimed result to a self-referential definition, a fitted input renamed as prediction, or a load-bearing self-citation chain. The derivation chain is self-contained against external benchmarks (exact diagonalization and time evolution) and does not invoke uniqueness theorems or ansatze from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics, Floquet theory for periodically driven systems, and numerical diagonalization of finite-size Hamiltonians; no additional free parameters, ad-hoc axioms, or new postulated entities are introduced in the abstract.

axioms (2)

standard math Floquet theory applies and the time-evolution operator can be diagonalized to obtain quasi-energies and eigenstates.
Implicit in the identification of π-spectral pairing and Floquet states.
domain assumption Finite-size numerical simulations faithfully capture the relevant spectral and dynamical features for the system sizes considered.
Required for the reported observations and scaling analysis.

pith-pipeline@v0.9.0 · 5501 in / 1351 out tokens · 42415 ms · 2026-05-09T23:32:48.892999+00:00 · methodology

discussion (0)

Reference graph

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