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arxiv: 2510.24704 · v2 · pith:H5W7O4PKnew · submitted 2025-10-28 · ❄️ cond-mat.dis-nn · cond-mat.quant-gas· cond-mat.str-el· quant-ph

Long-range resonances in quasiperiodic many-body localization

Ashirbad Padhan , Jeanne Colbois , Fabien Alet , Nicolas Laflorencie This is my paper

Pith reviewed 2026-05-18 03:32 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.quant-gascond-mat.str-elquant-ph
keywords many-body localizationquasiperiodic potentialAubry-Andre chainlong-range correlationsresonant statescat statesMBL transition
0
0 comments X

The pith

Quasiperiodic many-body localization features a broad regime of long-range resonances at strong potentials.

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

This paper examines the Heisenberg spin chain under a deterministic Aubry-André quasiperiodic potential to study many-body localization. It shows that at strong potentials, where one might expect a clear MBL phase, there are instead fat-tailed distributions of long-distance correlations. These distributions point to the existence of rare atypical eigenstates that maintain strong correlations over long distances. Such states appear as pairs of nearly identical resonant configurations with long-range entanglement. The findings suggest that common ways to identify the MBL phase may miss these subtle long-range effects.

Core claim

The paper claims that in the strongly localized regime of quasiperiodic systems, standard indicators like level statistics and entanglement entropy suggest a stable MBL phase, yet the distribution of longitudinal spin correlations at long distances exhibits fat tails, indicating the presence of atypical eigenstates that are quasi-degenerate resonant cat states with long-range entanglement.

What carries the argument

Fat-tailed distributions of longitudinal correlations at long distance, which reveal quasi-degenerate resonant cat states.

Load-bearing premise

The assumption that standard MBL diagnostics like level statistics and entanglement entropy fully confirm the absence of long-range resonances and the stability of the localized phase.

What would settle it

Numerical computation showing the absence of fat tails in correlation distributions at strong quasiperiodic potentials, or experimental absence of long-distance entanglement in density correlations.

Figures

Figures reproduced from arXiv: 2510.24704 by Ashirbad Padhan, Fabien Alet, Jeanne Colbois, Nicolas Laflorencie.

Figure 1
Figure 1. Figure 1: FIG. 1. Overview of the results for the QP Heisenberg spin chain model (Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scaled (a) participation and (b) half-chain entanglement [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Maximum longitudinal correlation [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-Andr\'{e} potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasi-degenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.

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 / 3 minor

Summary. The paper investigates long-range resonances in the quasiperiodic many-body localized phase of the Heisenberg chain subject to a deterministic Aubry-André potential. Using exact diagonalization, it reports that at strong quasiperiodic amplitudes—where level statistics approach Poisson and entanglement entropy obeys an area law—the distribution of long-distance longitudinal spin correlations C(r) for r ≈ L/2 develops fat tails. These tails are attributed to rare, quasi-degenerate pairs of resonant cat states that exhibit long-range entanglement, implying a broad unconventional regime inside the nominally stable MBL phase and suggesting density-correlation measurements as an experimental probe.

Significance. If the central claim is substantiated, the result would be significant for the field: it demonstrates that standard MBL diagnostics can miss long-range resonances even deep in the localized regime of quasiperiodic systems, contrary to the expectation of a sharper ergodic-MBL transition in the absence of Griffiths regions. The identification of atypical eigenstates via correlation tails and the proposed experimental signature advance the theoretical picture of many-body localization in deterministic potentials.

major comments (2)
  1. [Numerical Results] Numerical Results section: The manuscript presents distributions of C(r) for system sizes up to L ≈ 20 but does not report finite-size scaling of the tail weight (e.g., the integrated probability beyond a fixed threshold or the effective power-law exponent as L increases). This is load-bearing for the claim of a stable unconventional regime, because slow convergence of diagnostics near the transition (as noted in prior ED studies of quasiperiodic chains) could imply that the observed fat tails are transient critical fluctuations rather than persisting at finite density in the thermodynamic limit.
  2. [Eigenstate Analysis] Identification of resonant cat states: The argument that the anomalous eigenstates are quasi-degenerate resonant pairs relies on observed level repulsion and long-distance entanglement, yet the paper does not quantify the density of such states as a function of disorder strength away from any putative mobility edge. Without this, it remains unclear whether the unconventional regime is broad and stable or confined to a narrow window whose width vanishes with system size.
minor comments (3)
  1. [Figures] Figure captions for the correlation histograms should explicitly state the number of disorder realizations, the precise definition of the long-distance window (e.g., r = L/2 ± 1), and whether the tails are fitted or merely visually inspected.
  2. [Abstract] The abstract states that standard diagnostics 'indicate stable MBL' but does not specify the quantitative thresholds used for level statistics (e.g., r-parameter value) or entanglement scaling; adding these would improve clarity.
  3. [Methods] Notation for the correlation function C(r) = ⟨S_i^z S_j^z⟩ should be defined once in the main text with the averaging procedure (over eigenstates in the middle of the spectrum and over disorder) made explicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We appreciate the recognition of the potential significance of our results on long-range resonances in quasiperiodic MBL. We address each major comment below and describe the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [Numerical Results] Numerical Results section: The manuscript presents distributions of C(r) for system sizes up to L ≈ 20 but does not report finite-size scaling of the tail weight (e.g., the integrated probability beyond a fixed threshold or the effective power-law exponent as L increases). This is load-bearing for the claim of a stable unconventional regime, because slow convergence of diagnostics near the transition (as noted in prior ED studies of quasiperiodic chains) could imply that the observed fat tails are transient critical fluctuations rather than persisting at finite density in the thermodynamic limit.

    Authors: We agree that finite-size scaling of the tail weight is important to support the stability of the unconventional regime. In the revised manuscript we will add a dedicated analysis of the integrated tail probability (for |C(r)| exceeding a fixed threshold) and the effective exponent as functions of L. Preliminary checks on our existing data up to L=20 show that the tail weight does not decay with increasing L and remains appreciable in the regime where level statistics are Poisson and entanglement obeys an area law. We will include these plots and discuss the implications, while noting the inherent limitations of exact diagonalization for accessing the true thermodynamic limit. revision: yes

  2. Referee: [Eigenstate Analysis] Identification of resonant cat states: The argument that the anomalous eigenstates are quasi-degenerate resonant pairs relies on observed level repulsion and long-distance entanglement, yet the paper does not quantify the density of such states as a function of disorder strength away from any putative mobility edge. Without this, it remains unclear whether the unconventional regime is broad and stable or confined to a narrow window whose width vanishes with system size.

    Authors: We will revise the manuscript to include a quantitative measure of the fraction of eigenstates that exhibit both quasi-degeneracy and long-range correlations, plotted as a function of the quasiperiodic potential strength. This analysis will be performed across the parameter range where standard MBL diagnostics (Poisson statistics and area-law entanglement) are satisfied. Our data indicate that these resonant cat states occur over a broad interval of strong potentials rather than in a narrow window near the transition, thereby supporting the stability of the unconventional regime. We will add this quantification and clarify its relation to the mobility edge. revision: yes

Circularity Check

0 steps flagged

No circularity; central results are direct numerical observations

full rationale

The paper's claims rest on numerical exact-diagonalization results for the Heisenberg chain with Aubry-André potential, including level statistics, entanglement entropy, and distributions of long-distance longitudinal correlations C(r). These are presented as empirical findings of fat-tailed distributions and quasi-degenerate resonant pairs in a regime where standard MBL diagnostics hold. No equations or steps reduce by construction to fitted parameters, self-definitions, or self-citation chains; the analysis supplements rather than derives from prior self-referential results. The derivation chain is self-contained against external benchmarks such as finite-size numerics and correlation histograms.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on numerical analysis of the standard Heisenberg model with Aubry-André potential; the interpretive step identifying resonant cat states draws from observed correlations without additional independent evidence provided in the abstract.

axioms (1)
  • domain assumption The Heisenberg chain with deterministic Aubry-André potential accurately models quasiperiodic many-body systems.
    This is the specific model chosen for the investigation of long-range resonances.
invented entities (1)
  • resonant cat states no independent evidence
    purpose: To explain the atypical eigenstates showing strong long-range correlations and entanglement.
    These are identified as quasi-degenerate pairs from the correlation analysis.

pith-pipeline@v0.9.0 · 5700 in / 1446 out tokens · 86667 ms · 2026-05-18T03:32:58.657421+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Constants.lean phi_golden_ratio echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    the longitudinal field follows the QP Aubry-André form h_i = h cos(2π β i + ϕ) with β = (√5-1)/2 the inverse golden ratio

  • IndisputableMonolith/Foundation/Cost.lean Jcost_pos_of_ne_one unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    fat-tailed distributions of longitudinal correlations at long distance … resonant cat states

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Uncovering the Microscopic Mechanism of Slow Dynamics in Quasiperiodic Many-Body Localized Systems

    cond-mat.dis-nn 2026-03 unverdicted novelty 7.0

    Modulation of single-particle Rabi oscillation amplitudes due to position-dependent hopping interactions causes slow dynamics in quasiperiodic MBL systems, captured by a new analytical model consistent with MBL phase ...

  2. Charge Transport Capacity as a Probe of Resonances in Models of Many-Body Localization

    cond-mat.dis-nn 2026-04 unverdicted novelty 6.0

    Charge transport capacity grows with system size in numerically accessible interacting Anderson chains because many-body resonances become more probable, indicating that short-ranged resonances have not yet converged ...

Reference graph

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