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arxiv: 2507.18286 · v3 · submitted 2025-07-24 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech· quant-ph

Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath

Konrad Pawlik , Nicolas Laflorencie , Jakub Zakrzewski This is my paper

Pith reviewed 2026-05-19 03:21 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mechquant-ph
keywords many-body localizationergodicity breakingAnderson localizationentanglement entropyspectral statisticsquantum sun modelthermalizationrare events
0
0 comments X

The pith

A localized chain interacting with an ergodic bath develops volume-law entanglement with intermediate spectral statistics.

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

The paper examines thermalization in the interacting Anderson Quantum Sun model, where a localized chain couples to an ergodic bath. It identifies two regimes that depart from the expected link between spectral statistics and entanglement entropy. One regime combines volume-law entanglement with statistics that sit between Poisson and random-matrix behavior. The other shows Poisson statistics alongside sub-volume entanglement growth driven by rare events. A reader would care because these findings indicate new ways Anderson localization can break down without following the usual localized or fully ergodic pathways.

Core claim

In the interacting Anderson Quantum Sun model, standard localized phases with Poisson statistics and area-law entanglement coexist with ergodic phases, but two additional regimes appear: one with volume-law entanglement entropy together with intermediate spectral statistics, and another with Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations that signal emerging ergodic instabilities.

What carries the argument

The interacting Anderson Quantum Sun model, a localized chain coupled to an ergodic bath whose interplay produces the unconventional regimes.

If this is right

  • Volume-law entanglement can occur without fully random-matrix spectral statistics.
  • Poisson statistics can coexist with sub-volume entanglement when rare events dominate correlations.
  • Ergodic instabilities can nucleate inside localized systems through bath-induced rare events.
  • The conventional one-to-one mapping between level statistics and entanglement scaling does not hold in all hybrid localized-ergodic models.

Where Pith is reading between the lines

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

  • Comparable mixed regimes may appear in other models that couple a disordered chain to a weakly thermalizing environment.
  • Experimental probes in quantum simulators could search for the rare-event correlations as a signature of the second unconventional regime.
  • The stability of these phases in higher dimensions remains open and could be tested by extending the model geometry.

Load-bearing premise

The unconventional regimes are stable properties of the model in the thermodynamic limit rather than finite-size artifacts that would vanish for larger systems or different parameters.

What would settle it

Tensor-network or exact-diagonalization results on chains several times longer that show the volume-law regime with intermediate statistics collapsing into either fully Poisson or fully Wigner-Dyson behavior would indicate the reported phases are not stable.

Figures

Figures reproduced from arXiv: 2507.18286 by Jakub Zakrzewski, Konrad Pawlik, Nicolas Laflorencie.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the AQS model Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Phase diagram of the AQS model. (a): gap ratio extrapolated [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. High energy indicators of ergodicity-breaking, as a func [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Horizontal scan of the phase diagram at [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Multifractal dimension [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Histograms of rescaled correlation function [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

The study of many-body localized (MBL) phases intrinsically links spectral properties with eigenstate characteristics: localized systems exhibit Poisson level statistics and area-law entanglement entropy, while ergodic systems display volume-law entanglement and follow random matrix theory predictions, including level repulsion. Here, we introduce the interacting Anderson Quantum Sun model, which significantly deviates from these conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. These results highlight unconventional routes of ergodicity breaking and offer fresh perspectives on how Anderson localization may be destabilized.

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 paper introduces the interacting Anderson Quantum Sun model, a localized chain coupled to an ergodic bath. Numerical diagnostics reveal, beyond standard MBL (Poisson statistics, area-law entanglement) and ergodic (GOE statistics, volume-law entanglement) phases, two unconventional regimes: one with volume-law entanglement coexisting with intermediate spectral statistics, and another with Poisson statistics, sub-volume entanglement growth, and rare-event-dominated correlations signaling emerging ergodic instabilities.

Significance. If the reported regimes prove stable under thermodynamic-limit extrapolation and disorder averaging, the work would offer concrete numerical evidence for nonstandard routes to ergodicity breaking, extending the MBL paradigm and providing falsifiable predictions for how Anderson localization can be destabilized by ergodic baths.

major comments (2)
  1. [Numerical diagnostics and regime identification] The central claim that the two unconventional regimes constitute distinct, stable phases (rather than finite-size transients) is load-bearing for the abstract and conclusions, yet the manuscript provides no explicit finite-size scaling analysis or extrapolation to larger L; the reported behaviors could arise from slow relaxation or rare-region effects that drift toward conventional Poisson or GOE limits at accessible system sizes.
  2. [Results on spectral statistics and entanglement] The quantification of 'intermediate spectral statistics' and 'rare-event-dominated correlations' lacks error bars, disorder-sample statistics, or convergence checks with system size; without these, the distinction from standard phases remains provisional and cannot yet support the claim of unconventional thermalization routes.
minor comments (2)
  1. [Model definition] The definition of the interacting Anderson Quantum Sun model and the precise parameter ranges for each regime should be stated more explicitly in the introduction to aid reproducibility.
  2. [Figures] Figure captions and axis labels for entanglement and level-spacing plots could include the number of disorder realizations and the precise fitting windows used for spectral statistics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript introducing the interacting Anderson Quantum Sun model. We address the major comments point by point below, providing the strongest honest defense of our results while acknowledging where additional clarification or data strengthens the presentation.

read point-by-point responses

  1. Referee: [Numerical diagnostics and regime identification] The central claim that the two unconventional regimes constitute distinct, stable phases (rather than finite-size transients) is load-bearing for the abstract and conclusions, yet the manuscript provides no explicit finite-size scaling analysis or extrapolation to larger L; the reported behaviors could arise from slow relaxation or rare-region effects that drift toward conventional Poisson or GOE limits at accessible system sizes.

    Authors: We agree that explicit finite-size scaling is important to distinguish stable regimes from transients. In the revised manuscript we add scaling plots for entanglement entropy and spectral statistics across available system sizes, together with a discussion of why the observed volume-law/intermediate-statistics and Poisson/sub-volume regimes are consistent with stability rather than drift. Full thermodynamic-limit extrapolation is computationally prohibitive at present and is noted as future work; the current data nevertheless show no systematic drift toward conventional limits within the studied range. revision: partial

  2. Referee: [Results on spectral statistics and entanglement] The quantification of 'intermediate spectral statistics' and 'rare-event-dominated correlations' lacks error bars, disorder-sample statistics, or convergence checks with system size; without these, the distinction from standard phases remains provisional and cannot yet support the claim of unconventional thermalization routes.

    Authors: We accept this criticism and have revised all relevant figures to include error bars obtained from disorder averaging. The revised text now states the number of samples used at each size (hundreds for smaller L, fewer for larger L due to cost) and adds explicit convergence checks showing that the intermediate statistics and rare-event signatures remain stable with increasing L. These additions make the separation from conventional Poisson and GOE phases more quantitative. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on direct numerical diagnostics of a newly introduced model

full rationale

The paper introduces the interacting Anderson Quantum Sun model and reports numerical observations of entanglement scaling and spectral statistics across parameter regimes. These diagnostics are computed directly from exact diagonalization or similar methods on finite chains; no central claim reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation. The unconventional regimes are presented as empirical findings rather than derivations that presuppose their own outputs. External benchmarks (Poisson vs. GOE statistics, area vs. volume law) are standard and independent of the present results.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claims rest on numerical simulations of a newly introduced model whose parameters are selected to reveal non-standard behaviors; standard domain assumptions about MBL diagnostics are used as contrast.

free parameters (1)
  • interaction strength and disorder parameters
    Model parameters are tuned to access the reported unconventional regimes.
axioms (1)
  • domain assumption Localized systems exhibit Poisson level statistics and area-law entanglement while ergodic systems exhibit volume-law entanglement and random-matrix level repulsion.
    Invoked in the abstract to define conventional expectations against which new regimes are contrasted.
invented entities (1)
  • interacting Anderson Quantum Sun model no independent evidence
    purpose: To study unconventional thermalization of a localized chain with an ergodic bath
    New model introduced to deviate from standard MBL behavior.

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Forward citations

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  2. Graph-theory measures capture weak ergodicity breaking on large quantum systems

    quant-ph 2026-04 unverdicted novelty 6.0

    Graph-energy centrality detects weak ergodicity-breaking transitions in large quantum many-body systems via changes in its distribution and applies to kinetically constrained models showing glassy dynamics.

  3. Long-range resonances in quasiperiodic many-body localization

    cond-mat.dis-nn 2025-10 unverdicted novelty 6.0

    Quasiperiodic MBL systems host a broad unconventional regime with fat-tailed long-distance correlations and resonant cat states beyond what standard diagnostics detect.

Reference graph

Works this paper leans on

92 extracted references · 92 canonical work pages · cited by 2 Pith papers · 1 internal anchor

  1. [1]

    I. V . Gornyi, A. D. Mirlin, and D. G. Polyakov, Interacting Elec- trons in Disordered Wires: Anderson Localization and Low-T Transport, Phys. Rev. Lett.95, 206603 (2005)

    work page 2005

  2. [2]

    Basko, I

    D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transi- tion in a weakly interacting many-electron system with local- ized single-particle states, Annals of Physics321, 1126 (2006)

    work page 2006

  3. [3]

    Oganesyan and D

    V . Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B75, 155111 (2007)

    work page 2007

  4. [4]

    Pal and D

    A. Pal and D. A. Huse, Many-body localization phase transi- tion, Phys. Rev. B82, 174411 (2010)

    work page 2010

  5. [5]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-Body Localization and Thermalization in Quantum Statistical Mechanics, Annual Re- view of Condensed Matter Physics6, 15 (2015)

    work page 2015

  6. [6]

    Alet and N

    F. Alet and N. Laflorencie, Many-body localization: An intro- duction and selected topics, Comptes Rendus Physique19, 498 (2018)

    work page 2018

  7. [7]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Collo- quium: Many-body localization, thermalization, and entangle- ment, Rev. Mod. Phys.91, 021001 (2019)

    work page 2019

  8. [8]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Za- krzewski, Many-body localization in the age of classical com- puting, Reports on Progress in Physics88, 026502 (2025)

    work page 2025

  9. [9]

    J. M. Deutsch, Quantum statistical mechanics in a closed sys- tem, Phys. Rev. A43, 2046 (1991)

    work page 2046

  10. [10]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994)

    work page 1994

  11. [11]

    Rigol, V

    M. Rigol, V . Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854 EP (2008)

    work page 2008

  12. [12]

    D’Alessio, Y

    L. D’Alessio, Y . Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical me- chanics and thermodynamics, Advances in Physics65, 239 (2016)

    work page 2016

  13. [13]

    Serbyn, Z

    M. Serbyn, Z. Papi´c, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states, Phys. Rev. Lett.111, 127201 (2013)

    work page 2013

  14. [14]

    D. A. Huse, R. Nandkishore, and V . Oganesyan, Phenomenol- ogy of fully many-body-localized systems, Phys. Rev. B90, 174202 (2014)

    work page 2014

  15. [15]

    V . Ros, M. Mueller, and A. Scardicchio, Integrals of motion in the many-body localized phase, Nuclear Physics B891, 420 (2015)

    work page 2015

  16. [16]

    S. J. Thomson and M. Schiró, Time evolution of many-body localized systems with the flow equation approach, Phys. Rev. B97, 060201 (2018)

    work page 2018

  17. [17]

    D. J. Luitz, N. Laflorencie, and F. Alet, Many-body localization edge in the random-field Heisenberg chain, Phys. Rev. B91, 081103 (2015)

    work page 2015

  18. [18]

    Žnidari ˇc, A

    M. Žnidari ˇc, A. Scardicchio, and V . K. Varma, Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system, Phys. Rev. Lett.117, 040601 (2016)

    work page 2016

  19. [19]

    G. D. Chiara, S. Montangero, P. Calabrese, and R. Fazio, En- tanglement entropy dynamics of heisenberg chains, Journal of Statistical Mechanics: Theory and Experiment2006, P03001 (2006)

    work page 2006

  20. [20]

    Žnidari ˇc, T

    M. Žnidari ˇc, T. Prosen, and P. Prelovšek, Many-body localiza- tion in the Heisenberg XXZ magnet in a random field, Phys. Rev. B77, 064426 (2008)

    work page 2008

  21. [21]

    J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett.109, 017202 (2012)

    work page 2012

  22. [22]

    Serbyn, Z

    M. Serbyn, Z. Papi ´c, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems, Phys. Rev. Lett.110, 260601 (2013)

    work page 2013

  23. [23]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. V osk, E. Altman, U. Schneider, and I. Bloch, Ob- servation of many-body localization of interacting fermions in a quasirandom optical lattice, Science349, 842 (2015)

    work page 2015

  24. [24]

    Bordia, H

    P. Bordia, H. P. Lüschen, S. S. Hodgman, M. Schreiber, I. Bloch, and U. Schneider, Coupling identical one-dimensional many-body localized systems, Phys. Rev. Lett.116, 140401 (2016)

    work page 2016

  25. [25]

    Smith, A

    J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body lo- calization in a quantum simulator with programmable random disorder, Nature Physics12, 907 (2016)

    work page 2016

  26. [26]

    H. P. Lüschen, P. Bordia, S. Scherg, F. Alet, E. Altman, 6 U. Schneider, and I. Bloch, Observation of slow dynamics near the many-body localization transition in one-dimensional quasiperiodic systems, Phys. Rev. Lett.119, 260401 (2017)

    work page 2017

  27. [27]

    Léonard, S

    J. Léonard, S. Kim, M. Rispoli, A. Lukin, R. Schittko, J. Kwan, E. Demler, D. Sels, and M. Greiner, Probing the onset of quantum avalanches in a many-body localized system, Nature Physics19, 481 (2023)

    work page 2023

  28. [28]

    J. Z. Imbrie, Diagonalization and many-body localization for a disordered quantum spin chain, Phys. Rev. Lett.117, 027201 (2016)

    work page 2016

  29. [29]

    C. Yin, R. Nandkishore, and A. Lucas, Eigenstate localization in a many-body quantum system, Phys. Rev. Lett.133, 137101 (2024)

    work page 2024

  30. [30]

    W. D. Roeck, L. Giacomin, F. Huveneers, and O. Prosniak, Ab- sence of normal heat conduction in strongly disordered inter- acting quantum chains (2024), arXiv:2408.04338 [math-ph]

    work page arXiv 2024

  31. [31]

    C. L. Baldwin, Subballistic operator growth in spin chains with heavy-tailed random fields, Phys. Rev. B111, 184204 (2025)

    work page 2025

  32. [32]

    Šuntajs, J

    J. Šuntajs, J. Bon ˇca, T. Prosen, and L. Vidmar, Quantum chaos challenges many-body localization, Phys. Rev. E102, 062144 (2020)

    work page 2020

  33. [33]

    Weiner, F

    F. Weiner, F. Evers, and S. Bera, Slow dynamics and strong finite-size effects in many-body localization with random and quasiperiodic potentials, Phys. Rev. B100, 104204 (2019)

    work page 2019

  34. [34]

    Sierant, D

    P. Sierant, D. Delande, and J. Zakrzewski, Thouless time anal- ysis of anderson and many-body localization transitions, Phys. Rev. Lett.124, 186601 (2020)

    work page 2020

  35. [35]

    R. K. Panda, A. Scardicchio, M. Schulz, S. R. Taylor, and M. Znidaric, Can we study the many-body localisation transi- tion?, Europhysics Letters128, 67003 (2020)

    work page 2020

  36. [36]

    Sels and A

    D. Sels and A. Polkovnikov, Dynamical obstruction to local- ization in a disordered spin chain, Phys. Rev. E104, 054105 (2021)

    work page 2021

  37. [37]

    Kiefer-Emmanouilidis, R

    M. Kiefer-Emmanouilidis, R. Unanyan, M. Fleischhauer, and J. Sirker, Evidence for unbounded growth of the number en- tropy in many-body localized phases, Phys. Rev. Lett.124, 243601 (2020)

    work page 2020

  38. [38]

    Sierant, M

    P. Sierant, M. Lewenstein, and J. Zakrzewski, Polynomially fil- tered exact diagonalization approach to many-body localiza- tion, Phys. Rev. Lett.125, 156601 (2020)

    work page 2020

  39. [39]

    Abanin, J

    D. Abanin, J. Bardarson, G. D. Tomasi, S. Gopalakrish- nan, V . Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Annals of Physics427, 168415 (2021)

    work page 2021

  40. [40]

    Kiefer-Emmanouilidis, R

    M. Kiefer-Emmanouilidis, R. Unanyan, M. Fleischhauer, and J. Sirker, Unlimited growth of particle fluctuations in many- body localized phases, Annals of Physics435, 168481 (2021), special Issue on Localisation 2020

    work page 2021

  41. [41]

    Ghosh and M

    R. Ghosh and M. Žnidari ˇc, Resonance-induced growth of num- ber entropy in strongly disordered systems, Phys. Rev. B105, 144203 (2022)

    work page 2022

  42. [42]

    Sels, Bath-induced delocalization in interacting disordered spin chains, Phys

    D. Sels, Bath-induced delocalization in interacting disordered spin chains, Phys. Rev. B106, L020202 (2022)

    work page 2022

  43. [43]

    Sierant and J

    P. Sierant and J. Zakrzewski, Challenges to observation of many-body localization, Phys. Rev. B105, 224203 (2022)

    work page 2022

  44. [44]

    Sels and A

    D. Sels and A. Polkovnikov, Thermalization of dilute impuri- ties in one-dimensional spin chains, Phys. Rev. X13, 011041 (2023)

    work page 2023

  45. [45]

    Morningstar, L

    A. Morningstar, L. Colmenarez, V . Khemani, D. J. Luitz, and D. A. Huse, Avalanches and many-body resonances in many- body localized systems, Phys. Rev. B105, 174205 (2022)

    work page 2022

  46. [46]

    Laflorencie, G

    N. Laflorencie, G. Lemarié, and N. Macé, Chain breaking and Kosterlitz-Thouless scaling at the many-body localization tran- sition in the random-field Heisenberg spin chain, Phys. Rev. Re- search2, 042033 (2020)

    work page 2020

  47. [47]

    Šuntajs, J

    J. Šuntajs, J. Bon ˇca, T. Prosen, and L. Vidmar, Ergodicity breaking transition in finite disordered spin chains, Phys. Rev. B102, 064207 (2020)

    work page 2020

  48. [48]

    D. J. Luitz and Y . B. Lev, Absence of slow particle transport in the many-body localized phase, Phys. Rev. B102, 100202 (2020)

    work page 2020

  49. [49]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, and J. Zakrzewski, Stability of many-body localization in floquet systems, Phys. Rev. B107, 115132 (2023)

    work page 2023

  50. [50]

    Szołdra, P

    T. Szołdra, P. Sierant, M. Lewenstein, and J. Zakrzewski, Track- ing locality in the time evolution of disordered systems, Phys. Rev. B107, 054204 (2023)

    work page 2023

  51. [51]

    De Roeck and F

    W. De Roeck and F. Huveneers, Stability and instability towards delocalization in many-body localization systems, Phys. Rev. B 95, 155129 (2017)

    work page 2017

  52. [52]

    D. J. Luitz, F. Huveneers, and W. De Roeck, How a small quan- tum bath can thermalize long localized chains, Phys. Rev. Lett. 119, 150602 (2017)

    work page 2017

  53. [53]

    Potirniche, S

    I.-D. Potirniche, S. Banerjee, and E. Altman, Exploration of the stability of many-body localization ind >1, Phys. Rev. B99, 205149 (2019)

    work page 2019

  54. [54]

    P. J. D. Crowley and A. Chandran, Avalanche induced coexist- ing localized and thermal regions in disordered chains, Phys. Rev. Res.2, 033262 (2020)

    work page 2020

  55. [55]

    P. J. D. Crowley and A. Chandran, Mean-field theory of failed thermalizing avalanches, Phys. Rev. B106, 184208 (2022)

    work page 2022

  56. [56]

    Szołdra, P

    T. Szołdra, P. Sierant, M. Lewenstein, and J. Zakrzewski, Catch- ing thermal avalanches in the disordered xxz model, Phys. Rev. B109, 134202 (2024)

    work page 2024

  57. [57]

    Colmenarez, D

    L. Colmenarez, D. J. Luitz, and W. De Roeck, Ergodic in- clusions in many-body localized systems, Phys. Rev. B109, L081117 (2024)

    work page 2024

  58. [58]

    Berger, A

    V . Berger, A. Nava, J. H. Bardarson, and C. Artiaco, Numeri- cal study of disordered noninteracting chains coupled to a local lindblad bath (2024), arXiv:2412.03233 [cond-mat.dis-nn]

    work page arXiv 2024

  59. [59]

    Šuntajs and L

    J. Šuntajs and L. Vidmar, Ergodicity breaking transition in zero dimensions, Phys. Rev. Lett.129, 060602 (2022)

    work page 2022

  60. [60]

    Pawlik, P

    K. Pawlik, P. Sierant, L. Vidmar, and J. Zakrzewski, Many- body mobility edge in quantum sun models, Phys. Rev. B109, L180201 (2024)

    work page 2024

  61. [61]

    De Roeck, F

    W. De Roeck, F. Huveneers, M. Müller, and M. Schiulaz, Ab- sence of many-body mobility edges, Phys. Rev. B93, 014203 (2016)

    work page 2016

  62. [62]

    Šuntajs, M

    J. Šuntajs, M. Hopjan, W. De Roeck, and L. Vidmar, Similarity between a many-body quantum avalanche model and the ultra- metric random matrix model, Phys. Rev. Res.6, 023030 (2024)

    work page 2024

  63. [63]

    ´Swie ¸tek, P

    R. ´Swie ¸tek, P. Łyd˙zba, and L. Vidmar, Fading ergodicity meets maximal chaos, Phys. Rev. B111, 184203 (2025)

    work page 2025

  64. [64]

    Fleishman and P

    L. Fleishman and P. W. Anderson, Interactions and the Ander- son transition, Phys. Rev. B21, 2366 (1980)

    work page 1980

  65. [65]

    Haake,Quantum Signatures of Chaos(Springer, Berlin, 2010)

    F. Haake,Quantum Signatures of Chaos(Springer, Berlin, 2010)

    work page 2010

  66. [66]

    Serbyn and J

    M. Serbyn and J. E. Moore, Spectral statistics across the many- body localization transition, Phys. Rev. B93, 041424 (2016)

    work page 2016

  67. [67]

    Sierant and J

    P. Sierant and J. Zakrzewski, Level statistics across the many- body localization transition, Phys. Rev. B99, 104205 (2019)

    work page 2019

  68. [68]

    Łyd ˙zba, R

    P. Łyd ˙zba, R. ´Swi˛ etek, M. Mierzejewski, M. Rigol, and L. Vid- mar, Normal weak eigenstate thermalization, Phys. Rev. B110, 104202 (2024)

    work page 2024

  69. [69]

    Certain General Constraints on the Many-Body Localization Transition

    T. Grover, Certain general constraints on the many-body local- ization transition (2014), arXiv:1405.1471 [cond-mat.dis-nn]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  70. [70]

    C. Monthus, Many-body-localization transition: strong multi- 7 fractality spectrum for matrix elements of local operators, Jour- nal of Statistical Mechanics: Theory and Experiment2016, 073301 (2016)

    work page 2016

  71. [71]

    P. T. Dumitrescu, A. Goremykina, S. A. Parameswaran, M. Ser- byn, and R. Vasseur, Kosterlitz-thouless scaling at many-body localization phase transitions, Phys. Rev. B99, 094205 (2019)

    work page 2019

  72. [72]

    Evers, I

    F. Evers, I. Modak, and S. Bera, Internal clock of many-body delocalization, Phys. Rev. B108, 134204 (2023)

    work page 2023

  73. [73]

    Colbois, F

    J. Colbois, F. Alet, and N. Laflorencie, Interaction-driven in- stabilities in the random-fieldxxzchain, Phys. Rev. Lett.133, 116502 (2024)

    work page 2024

  74. [74]

    Colbois, F

    J. Colbois, F. Alet, and N. Laflorencie, Statistics of systemwide correlations in the random-field xxz chain: Importance of rare events in the many-body localized phase, Phys. Rev. B110, 214210 (2024)

    work page 2024

  75. [75]

    Biroli, A

    G. Biroli, A. K. Hartmann, and M. Tarzia, Large-deviation anal- ysis of rare resonances for the many-body localization transi- tion, Phys. Rev. B110, 014205 (2024)

    work page 2024

  76. [76]

    Laflorencie, J

    N. Laflorencie, J. Colbois, and F. Alet, Cat states carrying long- range correlations in the many-body localized phase (2025), arXiv:2504.10566 [cond-mat.dis-nn]

    work page arXiv 2025

  77. [77]

    (3) yields an average lo- calization length, averaged over the density of single-particle states, see Ref

    The phenomenological expression Eq. (3) yields an average lo- calization length, averaged over the density of single-particle states, see Ref. [88]

    work page

  78. [78]

    [88],W 0 slightly varies withW/J, from1.13 at strong disorder to1.22at weak disorder

    As noted in Ref. [88],W 0 slightly varies withW/J, from1.13 at strong disorder to1.22at weak disorder

    work page

  79. [79]

    Y . Y . Atas, E. Bogomolny, O. Giraud, and G. Roux, Distribu- tion of the ratio of consecutive level spacings in random matrix ensembles, Phys. Rev. Lett.110, 084101 (2013)

    work page 2013

  80. [80]

    Giraud, N

    O. Giraud, N. Macé, E. Vernier, and F. Alet, Probing symme- tries of quantum many-body systems through gap ratio statis- tics, Phys. Rev. X12, 011006 (2022)

    work page 2022

Showing first 80 references.