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REVIEW 5 major objections 5 minor 93 references

Particle-number entropy reveals thermal avalanches that two-point correlations miss entirely in a quasiperiodic XXZ chain, showing that correlation-based avalanche diagnostics are unreliable in quasiperiodic systems.

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2026-08-01 06:54 UTC pith:UBZPFSAH

load-bearing objection A useful numerical caution about correlation-based avalanche diagnostics in quasiperiodic systems, but the central 'avalanche' identification rests on small-system S_N signals that haven't been separated from finite-size thermalization. the 5 major comments →

arxiv 2607.21708 v1 pith:UBZPFSAH submitted 2026-07-23 cond-mat.dis-nn cond-mat.quant-gascond-mat.stat-mechcond-mat.str-el

Thermal avalanches in a quasiperiodic XXZ model

Paolo Molignini , Antonio \v{S}trkalj This is my paper
classification cond-mat.dis-nn cond-mat.quant-gascond-mat.stat-mechcond-mat.str-el PACS 72.15.Rn71.30.+h
keywords thermal avalanchesmany-body localizationquasiperiodic potentialXXZ spin chainparticle-number entropycorrelation lengthlocal integrals of motionquantum thermalization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether the thermal-avalanche mechanism, by which a small ergodic region can eat its way through a many-body-localized system, operates in a quasiperiodic spin chain the same way it does in a randomly disordered one. The authors couple a quasiperiodically localized XXZ chain to a small thermal bath and follow the dynamics with two complementary probes. They find a sharp disagreement: the two-point correlation function grows only logarithmically and yields local-integral-of-motion localization lengths below the avalanche threshold for every potential strength studied, while the particle-number entropy shows a delayed secondary growth that signals an avalanche front reaching the far end of the localized region whenever the bath is large enough. The claim is that in quasiperiodic systems, correlation-based avalanche detection can give false negatives, and that the standard analytic avalanche framework needs revision to account for short-range resonances of the quasiperiodic potential.

Core claim

For the quasiperiodic XXZ chain with an implanted thermal bath (bath field strength W_B = 0.5), the correlation length extracted from the bath-averaged two-point connected correlator grows logarithmically in time and maps to LIOM localization lengths that stay below the analytic avalanche threshold ξ_crit = 2/ln2 ≈ 2.9 for all W_A ≥ 2.5 and for both a small (L_B = 2) and a large (L_B = 8) bath. Under the standard reading of this observable, the avalanche dies out. The particle-number entropy S_N, which directly tracks transport of the conserved particle number across a partition boundary, contradicts that reading: for W_A ≲ 4 with L_B ≥ 4, S_N shows the hallmark two-stage growth, a bath-ther

What carries the argument

The argument runs on two observables and one analytical threshold. The avalanche threshold ξ_crit = 2/ln2 ≈ 2.9 comes from the standard hybridization condition: a thermal inclusion of size L_B grows when its coupling to a neighboring local integral of motion, decaying as e^{-Δx/ξ}, beats the many-body level spacing of the enlarged bath, which scales as 2^{-(L_B+Δx)/2}, so localization is destroyed when ξ exceeds 2/ln2. The correlation length ξ_d, extracted from the exponential spatial decay of the bath-averaged connected correlator and related to the LIOM localization length through ξ_d = (ξ/2) ln t, is the diagnostic that fails. The particle-number entropy S_N, obtained by decomposing the r

Load-bearing premise

The central claim rests on identifying the secondary rise of the particle-number entropy, which appears after the initial bath-thermalization plateau, as the arrival of a self-sustaining avalanche front rather than a finite-size artifact of thermalizing a 16-site chain with an 8-site thermal seed.

What would settle it

Simulate the same setup on longer chains (for instance L = 24 to 30 with an L_B = 8 bath) using a method that reaches those sizes, and check whether the S_N secondary rise propagates with arrival times t_{Δx} that grow exponentially in distance with ξ around 2.3, which would confirm a true avalanche front, or instead rises simultaneously at all partitions, which would indicate global small-chain thermalization. In a cold-atom realization of the quasiperiodic XXZ chain with an engineered low-disorder seed, the paper predicts a clear delayed rise of the number entropy across a mid-chain partitio

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If this is right

  • In quasiperiodic MBL systems, a logarithmically growing two-point correlation length is not evidence that an avalanche has terminated; correlation-only studies can produce false-negative avalanche verdicts.
  • Experiments on quasiperiodic systems should pair correlation-spreading measurements with the particle-number entropy or another transport-sensitive observable when judging whether a thermal inclusion destabilizes localization.
  • The analytic avalanche criterion ξ_crit ≈ 2.9 does not transfer unchanged to quasiperiodic systems: short-range resonances appear to renormalize the effective LIOM-bath coupling, effectively lowering the critical localization length.
  • Avalanche proliferation in this model retains the expected qualitative bath-size dependence (baths with L_B ≥ 4 sustain it at W_A = 3.0 while L_B = 2 does not), consistent with the positive-feedback picture, but quantitative agreement with avalanche theory remains imperfect.

Where Pith is reading between the lines

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

  • A natural testable extension is to repeat the protocol for other quasiperiodic families (Fibonacci modulation, off-diagonal Aubry-Andre variants), which organize resonances differently; the paper's mechanism would predict the size of the entropy-correlation gap to change accordingly.
  • The authors leave implicit that earlier experiments which inferred the absence of avalanches in quasiperiodic lattices from correlation spreading alone may need to be revisited with number-entropy or imbalance observables before concluding that quasiperiodic MBL is stable.
  • The front-arrival-time estimate ξ_S ≈ 2.3 at W_A = 3.0 sits close to ξ_crit, suggesting the system may lie near the avalanche boundary there; resolving whether the front slows exponentially with distance (dying avalanche) or propagates at steady pace (true runaway) at larger sizes would sharpen the verdict.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper studies bath-induced thermalization (quantum avalanches) in a quasiperiodic XXZ spin chain with an engineered thermal inclusion. Using exact diagonalization for systems up to L=18, the authors compare two observables: the bath-averaged two-point correlation function g^(2), from which they extract a time-dependent correlation length ξ_d(t) and, via Eq. (22), a LIOM localization length ξ; and the particle-number entropy S_N across three partitions. The central claim is that these observables give opposite answers in the quasiperiodic case: correlations grow only logarithmically and yield ξ values well below the avalanche threshold ξ_crit≈2.9 for all W_A≥2.5, while S_N shows a secondary growth interpreted as an avalanche front reaching distant partitions for W_A≲4 and L_B≥4. The authors conclude that two-point correlations are unreliable diagnostics of thermal avalanches in quasiperiodic systems and that the standard avalanche framework requires revision to account for short-range quasiperiodic resonances. Appendices provide finite-size checks for ξ_d, a comparison with the ergodic side, and a random-bath control.

Significance. If the central claim holds, the paper has clear significance for both theory and experiment: it identifies a concrete observable (particle-number entropy) that detects quasiperiodic avalanches when correlation-spreading measurements would give a false negative, with direct implications for ultracold-atom experiments following Ref. [44]. The paper is also careful in several respects: it performs disorder averaging over many phase realizations, it subtracts the no-bath baseline to control for intrinsic quasiperiodic resonance-induced growth, it checks that a random bath gives nearly identical correlation dynamics, and it examines both bath-size and potential-strength dependence. These controls lend internal consistency to the numerics. However, the central quantitative claim that S_N identifies a true self-sustaining avalanche—and not finite-size global thermalization—rests on small systems (L=16, L_A=8) with only three partition distances, and the correlation-based ξ extraction is partly circular because it uses the very avalanche theory being tested. The conclusion is plausible but requires stronger finite-size and statistical support.

major comments (5)
  1. [§V.B, Figs. 5–7] The load-bearing identification of the secondary S_N rise as an avalanche front is not adequately separated from finite-size global thermalization. The systems have L=16 with L_A=8 and L_B=8; W_A=3.0 is near/inside the finite-size MBL crossover for quasiperiodic chains. The no-bath subtraction controls for intrinsic resonance-driven growth, but it does not control for the possibility that a sufficiently strong bath simply thermalizes the whole small chain without a self-sustaining avalanche. Appendix A checks finite-size effects only for ξ_d, not for S_N. I request an L_A scan (e.g., L_A=10,12,14 with L_B fixed, or at least L=18 as in Appendix A) for the S_N curves, or a demonstration that front-arrival times grow exponentially in Δx over at least 3–4 intervals and are independent of L_A. Without this, the discrepancy between S_N and ξ_d could be a small-system artifact.
  2. [§V.A and Eq. (22)] The extraction of the LIOM localization length ξ from the correlation length uses Eq. (22), ξ_d = (ξ/2) ln t + const, which is precisely the relation derived from the exponential-coupling/Fermi-golden-rule picture of Ref. [29] that the paper aims to test. Concluding 'no avalanche because ξ<ξ_crit' from this fit is therefore partially circular. The independent S_N observable mitigates this, but the quantitative claim that ξ≈0.4 at W_A=3 is not an independent measurement of the LIOM localization length. The authors should either validate Eq. (22) for their model by an independent method (e.g., LIOM construction or spectral statistics), or explicitly reframe the ξ values as effective fit parameters rather than LIOM lengths.
  3. [§V.A, Fig. 4] The central quantitative assertion that ξ remains below ξ_crit for all W_A≥2.5 rests on linear fits of ξ_d(t) over the ad hoc interval t∈[10,1000], with no error bars, no fit-quality measures, and no sensitivity analysis. Only about two decades of logarithmic growth are fitted, and for W_A={2.5,3.0,3.5} the curves visibly bend over after t∼1000 (attributed to finite-size effects). The extracted slopes, and hence ξ, are likely sensitive to the chosen window. Please report confidence intervals, show representative fits, and test alternative fitting windows (e.g., t∈[20,500], t∈[10,5000] with saturation excluded differently). This is necessary before 'well below ξ_crit' can be taken as robust.
  4. [§V.B, Fig. 7 and text following] The front-arrival times are defined by an arbitrary ΔS_N cutoff (5% of maximum S_N, stated as 0.01 in the caption), and only three partitions (Δx=2,4,6) are used, giving two time ratios from which ξ_S≈{2.49,2.23} is estimated. No uncertainty on these arrival times is provided, and for W_A=5 the extraction uses t_6=∞. The statement that the S_N-derived ξ_S is 'comparable to the critical ξ_aval' is therefore only order-of-magnitude. I recommend reporting arrival-time uncertainties, using more partitions (if system size permits) or a different threshold dependence, and presenting the exponential-time fit with residuals. Otherwise the quantitative comparison with ξ_crit is not well supported.
  5. [§VI and Introduction] The paper concludes that 'the standard avalanche framework requires revision' for quasiperiodic systems, but it does not quantitatively benchmark against the existing quasiperiodic avalanche study of Ref. [49] (Tu, Vu, and Das Sarma). Given that Ref. [49] is cited earlier as the relevant prior work, the authors should explicitly compare their phase boundary, observables, and conclusions with that reference. Without such a comparison, the claim of a needed revision is not placed in the context of the current literature and appears stronger than the evidence presented.
minor comments (5)
  1. [§II] Typo: 'interaction strenghts' should be 'strengths'. Also the section heading 'Avalanche theory' in §III uses inconsistent capitalization.
  2. [§V.A and Fig. 4 captions] The text says the dashed lines in Figs. 4(a,c) are 'exponential fit', but the fit is linear in ln t via Eq. (22). Please reword to avoid confusion.
  3. [Appendix A, Fig. 8] The y-axis label 'ξ_d L' is ambiguous: is this ξ_d multiplied by L or ξ_d/L? The text says 'scaled by the system size' but the axis does not clarify. Also, the scaled quantity is not defined in the main text.
  4. [§V.B, Fig. 7] The threshold definition is inconsistent between the main text ('5% of the maximum value of S_N') and the caption ('ΔS_N=0.01'). If these are equivalent (e.g., because max S_N≈0.2 for the plotted cases), please state so explicitly.
  5. [§V.B] The term 'uniform system' is used for gray curves with W_B=W_A. Please define this term explicitly in the main text; it is not self-explanatory.

Circularity Check

0 steps flagged

No circular derivation; the central discrepancy is empirical and grounded in an independent observable. Minor self-citation in the speculative mechanism only.

full rationale

The paper's central claim is not a derivation that reduces to its inputs. The correlation-based conclusion ('no avalanche') is obtained by fitting ξ_d and using the standard avalanche-theory relation ξ_d = (ξ/2) ln t + const, Eq. (22), to extract ξ, then comparing ξ with ξ_crit ≈ 2.9. This is an application of the theory as a diagnostic, not a construction of the conclusion from itself. The independent particle-number entropy S_N is measured separately and shows secondary growth; the discrepancy between the two observables is an empirical falsification of the correlation-based diagnostic, not a tautology. The no-bath subtraction (gray curves in Fig. 5) and the L_B scan (Fig. 6) provide independent evidence that the secondary S_N growth is bath-induced, so the central claim does not rest on a fitted parameter renamed as a prediction. The proposed resonance mechanism cites Refs. [69,70], which include a co-author, but those citations support only the speculative explanation for the quantitative deviations; the central discrepancy stands on the computed S_N data. The main caveat—that with L=16, L_A=8, L_B=8 and W_A=3 near the finite-size MBL crossover, the S_N secondary growth could reflect global finite-size thermalization rather than a self-sustaining avalanche—is a correctness risk, not a circularity. Therefore no step reduces by construction; the minor self-citation in the mechanism discussion does not make the central claim circular.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

No invented entities: the paper introduces no new particles, forces, or conserved quantities. The free parameters are the setup choices (W_B, β, phases), the fitted ξ from the correlation-length slope, and the arbitrary threshold for front arrival. The axioms are the standard avalanche-theory ingredients plus the interpretive step that S_N growth equals avalanche propagation.

free parameters (4)
  • bath potential strength W_B = 0.5
    Fixed by hand to keep the bath ergodic (Sec. II); results could shift if W_B is varied.
  • LIOM localization length ξ from correlation fit = ≈0.4–2 (see Fig. 4)
    Extracted via linear fit of ξ_d vs ln t over fit interval t∈[10,1000] (Eq. 22); this fit is a free-parameter extraction, and its validity for quasiperiodic systems is itself in question.
  • threshold for front arrival ΔS_N = 5% of max S_N (≈0.01–0.06)
    Arbitrary cutoff used to define front-arrival times in Fig. 7; the ξ_S estimates depend on it.
  • correlation-fit interval = t ∈ [10,1000]
    Post-hoc choice to exclude late-time finite-size saturation (Sec. V.A and Appendix A); affects all reported ξ.
axioms (6)
  • domain assumption LIOM representation: existence of quasilocal integrals of motion with exponentially decaying weight Ω(n) ~ e^{-|j-k|/ξ}
    Assumed in Sec. III following Refs. [14,29]; the central correlation-based analysis relies on this representation being valid in the quasiperiodic system.
  • domain assumption ETH matrix-element ansatz for bath operator (Eq. 9)
    Standard avalanche theory from Ref. [29]; used to derive the critical ξ_crit = 2/ln2.
  • domain assumption Fermi's golden rule gives thermalization time t_j ∝ e^{2Δx/ξ} (Eq. 10)
    Basis for Eq. (22) connecting ξ_d and ξ.
  • domain assumption Bath (W_B=0.5) acts as a stationary infinite-temperature reservoir after t_B ~ 10
    Inferred from saturation of off-diagonal g^(2) in Fig. 3(a); the S_N interpretation of a later secondary growth as avalanche arrival depends on this.
  • ad hoc to paper The secondary growth of S_N in presence vs absence of bath marks avalanche-front arrival, not resonance-assisted transport or finite-size global thermalization
    Core interpretive step in Sec. V.B; the no-bath subtraction is evidence, but finite-size (L=16-18) and crossover proximity leave ambiguity.
  • ad hoc to paper Short-range resonances of the quasiperiodic potential renormalize LIOM–bath coupling v_{i,j}
    Speculative mechanism invoked to explain quantitative deviations (Sec. V.B, Conclusions), supported mainly by self-cited Refs. [69,70,73].

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Cite this review

Pith. "Pith review of Thermal avalanches in a quasiperiodic XXZ model." pith.science (2026). https://pith.science/paper/UBZPFSAH

@misc{pith2026260721708,
  author       = {Pith},
  title        = {Pith review of: Thermal avalanches in a quasiperiodic XXZ model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UBZPFSAH}},
  note         = {Machine review of arXiv:2607.21708}
}
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read the original abstract

We study bath-induced thermalization in the many-body localized XXZ spin chain subjected to a quasiperiodic magnetic field. We engineer a thermal inclusion by setting the field strength in one part of the chain below the localization threshold and analyze thermalization via the avalanche mechanism. To study the nature of such avalanches, we use two complementary observables, namely the two-point connected correlation function and the particle-number entropy. Surprisingly, the correlations alone show no signatures of avalanches. Instead, they display a logarithmic growth of the correlation length throughout the dynamics and predict localization lengths of the local integrals of motion that remain well below the avalanche threshold. In contrast, the particle number entropy shows clear signatures of the thermal avalanche, with the avalanche front progressively propagating deeper into the localized subsystem for sufficiently large baths. The discrepancy between the two observables shows that two-point correlations are unreliable in identifying thermal avalanches in quasiperiodic systems, as opposed to the random case. On one hand, qualitative results are consistent with the analytical predictions of the standard avalanche theory. On the other hand, significant quantitative deviations persist, which could be due to short-range resonances generated by the quasiperiodic potential. Our results suggest that the standard avalanche framework requires revision to account for the short-range correlations of quasiperiodic potentials.

Figures

Figures reproduced from arXiv: 2607.21708 by Antonio \v{S}trkalj, Paolo Molignini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a). We also observe faster-than-logarithmic growth of ξd in our numerics. However, this behavior appears only on the ergodic side of the crossover at lower potential strengths, as shown in Appendix B. This comparison indicates that faster-than-logarithmic growth reflects globally ergodic dynamics in our model, rather than being a necessary signature of avalanche proliferation within the localized regime. … view at source ↗
Figure 5
Figure 5. Figure 5: The hallmark secondary growth associated with avalanche propagation is now absent for all partition lo￾cations. Instead, the curves either display the continuous growth expected in the ergodic regime, e.g. for WA = 1.5, or closely follow the corresponding curves without the bath, as for WA = 3. This demonstrates that the bath is too small to sustain an avalanche, and its thermaliz￾ing influence remains con… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

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Works this paper leans on

93 extracted references · 1 canonical work pages

  1. [1]

    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

    1958

  2. [2]

    B. L. Altshuler, Y. Gefen, A. Kamenev, and L. S. Levitov, Quasiparticle lifetime in a finite system: A nonperturba- tive approach, Phys. Rev. Lett.78, 2803 (1997)

    1997

  3. [3]

    I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interact- ing electrons in disordered wires: Anderson localization and low-ttransport, Phys. Rev. Lett.95, 206603 (2005)

    2005

  4. [4]

    D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Metal–insulator transition in a weakly interacting many- electron system with localized single-particle states, An- nals of Physics321, 1126 (2006)

    2006

  5. [5]

    Oganesyan and D

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

    2007

  6. [6]

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

    2046

  7. [7]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E50, 888 (1994)

    1994

  8. [8]

    Srednicki, The approach to thermal equilibrium in quantized chaotic systems, Journal of Physics A: Math- ematical and General32, 1163 (1999)

    M. Srednicki, The approach to thermal equilibrium in quantized chaotic systems, Journal of Physics A: Math- ematical and General32, 1163 (1999)

    1999

  9. [9]

    Rigol, V

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

    2008

  10. [10]

    D’Alessio, Y

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

    2016

  11. [11]

    Gopalakrishnan and S

    S. Gopalakrishnan and S. Parameswaran, Dynamics and transport at the threshold of many-body localization, Physics Reports862, 1 (2020)

    2020

  12. [12]

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

    2014

  13. [13]

    Serbyn, Z

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

    2013

  14. [14]

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

    2015

  15. [15]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, An- nual Review of Condensed Matter Physics6, 15 (2015)

    2015

  16. [16]

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

    2016

  17. [17]

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

    2018

  18. [18]

    ˇZnidariˇ c, A

    M. ˇZnidariˇ c, 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)

    2016

  19. [19]

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

    2012

  20. [20]

    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)

    2013

  21. [21]

    Iemini, A

    F. Iemini, A. Russomanno, D. Rossini, A. Scardicchio, and R. Fazio, Signatures of many-body localization in the dynamics of two-site entanglement, Phys. Rev. B94, 214206 (2016)

    2016

  22. [22]

    Singh, J

    R. Singh, J. H. Bardarson, and F. Pollmann, Signatures of the many-body localization transition in the dynamics of entanglement and bipartite fluctuations, New Journal of Physics18, 023046 (2016)

    2016

  23. [23]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

    2019

  24. [24]

    Gopalakrishnan and D

    S. Gopalakrishnan and D. A. Huse, Instability of many- body localized systems as a phase transition in a non- standard thermodynamic limit, Phys. Rev. B99, 134305 (2019)

    2019

  25. [25]

    R. B. Griffiths, Nonanalytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23, 17 (1969)

    1969

  26. [26]

    Vojta, Quantum griffiths effects and smeared phase transitions in metals: Theory and experiment, Journal of Low Temperature Physics161, 299 (2010)

    T. Vojta, Quantum griffiths effects and smeared phase transitions in metals: Theory and experiment, Journal of Low Temperature Physics161, 299 (2010)

    2010

  27. [27]

    Agarwal, E

    K. Agarwal, E. Altman, E. Demler, S. Gopalakrishnan, D. A. Huse, and M. Knap, Rare-region effects and dy- namics near the many-body localization transition, An- nalen der Physik529, 10.1002/andp.201600326 (2017)

    doi:10.1002/andp.201600326 2017

  28. [28]

    W. D. Roeck and J. Z. Imbrie, Many-body localization: stability and instability, Philosophical Transactions of the Royal Society A375, 20160422 (2017)

    2017

  29. [29]

    De Roeck and F

    W. De Roeck and F. Huveneers, Stability and instabil- ity towards delocalization in many-body localization sys- tems, Phys. Rev. B95, 155129 (2017)

    2017

  30. [30]

    Thiery, F

    T. Thiery, F. Huveneers, M. M¨ uller, and W. De Roeck, Many-body delocalization as a quantum avalanche, Phys. Rev. Lett.121, 140601 (2018)

    2018

  31. [31]

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

    2017

  32. [32]

    Goihl, J

    M. Goihl, J. Eisert, and C. Krumnow, Exploration of the stability of many-body localized systems in the presence of a small bath, Phys. Rev. B99, 195145 (2019)

    2019

  33. [33]

    Morningstar, L

    A. Morningstar, L. Colmenarez, V. Khemani, D. J. Luitz, and D. A. Huse, Avalanches and many-body res- onances in many-body localized systems, Phys. Rev. B 105, 174205 (2022)

    2022

  34. [34]

    Colmenarez, D

    L. Colmenarez, D. J. Luitz, and W. De Roeck, Ergodic inclusions in many-body localized systems, Phys. Rev. B 14 109, L081117 (2024)

    2024

  35. [35]

    Szo ldra, P

    T. Szo ldra, P. Sierant, M. Lewenstein, and J. Zakrzewski, Catching thermal avalanches in disordered XXZ model, Phys. Rev. B109, 134202 (2024)

    2024

  36. [36]

    Goremykina, R

    A. Goremykina, R. Vasseur, and M. Serbyn, Analytically solvable renormalization group for the many-body local- ization transition, Phys. Rev. Lett.122, 040601 (2019)

    2019

  37. [37]

    P. T. Dumitrescu, A. Goremykina, S. A. Parameswaran, M. Serbyn, and R. Vasseur, Kosterlitz-thouless scaling at many-body localization phase transitions, Phys. Rev. B 99, 094205 (2019)

    2019

  38. [38]

    Morningstar and D

    A. Morningstar and D. A. Huse, Renormalization-group study of the many-body localization transition in one di- mension, Phys. Rev. B99, 224205 (2019)

    2019

  39. [39]

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

    2022

  40. [40]

    Scocco, G

    A. Scocco, G. Passarelli, M. Collura, P. Lucignano, and A. Russomanno, Thermalization propagation front and robustness against avalanches in localized systems, Phys. Rev. B110, 134204 (2024)

    2024

  41. [41]

    De Roeck, F

    W. De Roeck, F. Huveneers, B. Meeus, and A. O. Pro´ sniak, Rigorous and simple results on very slow ther- malization, or quasi-localization, of the disordered quan- tum chain, Physica A: Statistical Mechanics and its Ap- plications631, 129245 (2023)

    2023

  42. [42]

    Sels, Bath-induced delocalization in interacting disor- dered spin chains, Phys

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

    2022

  43. [43]

    H. Ha, A. Morningstar, and D. A. Huse, Many-body res- onances in the avalanche instability of many-body local- ization, Phys. Rev. Lett.130, 250405 (2023)

    2023

  44. [44]

    L´ eonard, S

    J. L´ eonard, 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, 10.1038/s41567-022-01887-3 (2023)

    work page doi:10.1038/s41567-022-01887-3 2023

  45. [45]

    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)

    2019

  46. [46]

    Agrawal, R

    U. Agrawal, R. Vasseur, and S. Gopalakrishnan, Quasiperiodic many-body localization transition in di- mension d>1, Phys. Rev. B106, 094206 (2022)

    2022

  47. [47]

    ˇStrkalj, E

    A. ˇStrkalj, E. V. H. Doggen, and C. Castelnovo, Coexis- tence of localization and transport in many-body two- dimensional Aubry-Andr´ e models, Phys. Rev. B106, 184209 (2022)

    2022

  48. [48]

    E. V. H. Doggen and A. D. Mirlin, Many-body delocaliza- tion dynamics in long Aubry-Andr´ e quasiperiodic chains, Phys. Rev. B100, 104203 (2019)

    2019

  49. [49]

    Y.-T. Tu, D. Vu, and S. Das Sarma, Avalanche stabil- ity transition in interacting quasiperiodic systems, Phys. Rev. B107, 014203 (2023)

    2023

  50. [50]

    E. V. H. Doggen, F. Schindler, K. S. Tikhonov, A. D. Mirlin, T. Neupert, D. G. Polyakov, and I. V. Gornyi, Many-body localization and delocalization in large quan- tum chains, Phys. Rev. B98, 174202 (2018)

    2018

  51. [51]

    Chanda, P

    T. Chanda, P. Sierant, and J. Zakrzewski, Time dynam- ics with matrix product states: Many-body localization transition of large systems revisited, Phys. Rev. B101, 035148 (2020)

    2020

  52. [52]

    Abrahams, P

    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Ab- sence of quantum diffusion in two dimensions, Phys. Rev. Lett.42, 673 (1979)

    1979

  53. [53]

    Biddle and S

    J. Biddle and S. D. Sarma, Predicted mobility edges in one-dimensional incommensurate optical lattices, Phys. Rev. Lett.104, 070601 (2010)

    2010

  54. [54]

    Ganeshan, J

    S. Ganeshan, J. H. Pixley, and S. D. Sarma, Nearest neighbor tight binding models with an exact mobility edge in one dimension, Phys. Rev. Lett.114, 146601 (2015)

    2015

  55. [55]

    H. P. L¨ uschen, P. Bordia, S. Scherg, F. Alet, E. Altman, U. Schneider, and I. Bloch, Single-particle mobility edge in a one-dimensional quasiperiodic optical lattice, Phys. Rev. Lett.120, 160404 (2018)

    2018

  56. [56]

    F. A. An, K. Padavi´ c, E. J. Meier, S. Hegde, S. Gane- shan, J. H. Pixley, S. Vishveshwara, and B. Gadway, In- teractions and mobility edges: Observing the general- ized Aubry–Andr´ e model, Phys. Rev. Lett.126, 040603 (2021)

    2021

  57. [57]

    Molignini, Stability of quasicrystalline ultracold fermions to dipolar interactions, Phys

    P. Molignini, Stability of quasicrystalline ultracold fermions to dipolar interactions, Phys. Rev. Research7, L032026 (2025)

    2025

  58. [58]

    Goblot, A

    V. Goblot, A. ˇStrkalj, N. Pernet, J. L. Lado, C. Dorow, A. Lema ˆ ıtre, L. Le Gratiet, A. Harouri, I. Sagnes, S. Ravets, A. Amo, J. Bloch, and O. Zilberberg, Emer- gence of criticality through a cascade of delocalization transitions in quasiperiodic chains, Nature Physics16, 832 (2020)

    2020

  59. [59]

    ˇStrkalj, E

    A. ˇStrkalj, E. V. H. Doggen, I. V. Gornyi, and O. Zilber- berg, Many-body localization in the interpolating Aubry- Andr´ e-Fibonacci model, Phys. Rev. Res.3, 033257 (2021)

    2021

  60. [60]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das paulische ¨ aquivalenzverbot, Zeitschrift f¨ ur Physik47, 631 (1928)

    1928

  61. [61]

    S. Iyer, V. Oganesyan, G. Refael, and D. A. Huse, Many- body localization in a quasiperiodic system, Phys. Rev. B87, 134202 (2013)

    2013

  62. [62]

    A. S. Aramthottil, T. Chanda, P. Sierant, and J. Za- krzewski, Finite-size scaling analysis of the many-body localization transition in quasiperiodic spin chains, Phys. Rev. B104, 214201 (2021)

    2021

  63. [63]

    P. R. N. Falc˜ ao, A. S. Aramthottil, P. Sierant, and J. Za- krzewski, Many-body localization crossover is sharper in a quasiperiodic potential, Phys. Rev. B110, 184209 (2024)

    2024

  64. [64]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. L¨ uschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Observation of many-body localization of inter- acting fermions in a quasirandom optical lattice, Science 349, 842 (2015)

    2015

  65. [65]

    Molignini, B

    P. Molignini, B. Dumont, and A. Thomas, EDITH: Exact diagonalization of interacting time-dependent hamiltoni- ans (2026), gitLab repository, accessed April 2026

    2026

  66. [66]

    De Roeck and F

    W. De Roeck and F. Huveneers, Scenario for delocaliza- tion in translation-invariant systems, Phys. Rev. B90, 165137 (2014)

    2014

  67. [67]

    ˇZnidariˇ c, T

    M. ˇZnidariˇ c, T. Prosen, and P. Prelovˇ sek, Many-body localization in the Heisenberg XXZ magnet in a random field, Phys. Rev. B77, 064426 (2008)

    2008

  68. [68]

    Ghosh and M

    R. Ghosh and M. ˇZnidariˇ c, Resonance-induced growth of number entropy in strongly disordered systems, Phys. Rev. B105, 144203 (2022)

    2022

  69. [69]

    Faulend, H

    B. Faulend, H. Buljan, and A. ˇStrkalj, Uncovering the microscopic mechanism of slow dynamics in quasiperiodic many-body localized systems (2026), arXiv:2603.28721

    Pith/arXiv arXiv 2026

  70. [70]

    Tabanelli, C

    H. Tabanelli, C. Castelnovo, and A. ˇStrkalj, Reentrant 15 localization transitions and anomalous spectral proper- ties in off-diagonal quasiperiodic systems, Phys. Rev. B 110, 184208 (2024)

    2024

  71. [71]

    Sierant and J

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

    2022

  72. [72]

    Kiefer-Emmanouilidis, R

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

    2020

  73. [73]

    Padhan, J

    A. Padhan, J. Colbois, F. Alet, and N. Laflorencie, Long- range resonances in quasiperiodic many-body localiza- tion, Phys. Rev. Lett.136, 197101 (2026)

    2026

  74. [74]

    J.-y. Choi, S. Hild, J. Zeiher, P. Schauss, A. Rubio- Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Exploring the many-body localization transition in two dimensions, Science352, 1547 (2016)

    2016

  75. [75]

    Bordia, H

    P. Bordia, H. L¨ uschen, S. Scherg, S. Gopalakrishnan, M. Knap, U. Schneider, and I. Bloch, Probing slow re- laxation and many-body localization in two-dimensional quasiperiodic systems, Phys. Rev. X7, 041047 (2017)

    2017

  76. [76]

    J. Hur, J. Li, B. Lee, K. Kwon, M. Kim, S. Hwang, S. Kim, Y. S. Yu, A. Chan, T. Wahl, and J. yoon Choi, Stability of many-body localization in two dimensions (2025), arXiv:2508.20699 [cond-mat.quant-gas]

    Pith/arXiv arXiv 2025

  77. [77]

    N. Y. Yao, C. R. Laumann, S. Gopalakrishnan, M. Knap, M. M¨ uller, E. A. Demler, and M. D. Lukin, Many-body localization in dipolar systems, Physical Review Letters 113, 243002 (2014)

    2014

  78. [78]

    R. M. Nandkishore and S. L. Sondhi, Many-body local- ization with long-range interactions, Physical Review X 7, 041021 (2017)

    2017

  79. [79]

    Nag and A

    S. Nag and A. Garg, Many-body localization in the pres- ence of long-range interactions and long-range hopping, Physical Review B99, 224203 (2019)

    2019

  80. [80]

    X. Deng, G. Masella, G. Pupillo, and L. Santos, Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions, Physical Review Letters125, 010401 (2020)

    2020

Showing first 80 references.