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arxiv: 2605.00094 · v2 · submitted 2026-04-30 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Recognition: 2 theorem links

· Lean Theorem

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

Heiko Georg Menzler , Rafa{\l} \'Swi\k{e}tek , Mari Carmen Ba\~nuls , Fabian Heidrich-Meisner
Authors on Pith no claims yet

Pith reviewed 2026-05-12 05:24 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el
keywords weak ergodicity breakingFock space graphgraph-energy centralityquantum many-body systemskinetically constrained modelsthermodynamic limitglassy dynamicscentrality measures
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The pith

Graph-energy centrality on Fock-space graphs detects weak ergodicity-breaking transitions through shifts in its distribution.

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

The paper establishes that weak ergodicity violations in closed quantum many-body systems, occurring at parameter-controlled transitions, can be tracked using graph-theoretic tools on the system's Fock-space representation. The key finding is that graph-energy centrality shows distinct changes in its probability distribution exactly at these transition points. This method scales analytically to systems of hundreds of sites and sometimes the thermodynamic limit, bypassing the size restrictions of most existing numerical approaches. The approach is illustrated on a kinetically constrained model that also exhibits glassy dynamics near the transition.

Core claim

Representing a quantum many-body system as a graph in Fock space and computing the graph-energy centrality on that graph produces a distribution whose characteristic changes mark the onset of weak ergodicity breaking at known transition points, allowing the same diagnostic to be applied analytically to systems far larger than those accessible by standard exact methods.

What carries the argument

Graph-energy centrality computed on the Fock-space graph of the Hamiltonian, which registers the relative importance of basis states according to their connectivity and energy structure.

If this is right

  • The same measure can be evaluated analytically for quantum systems containing hundreds of sites.
  • In selected cases the calculation extends directly to the thermodynamic limit.
  • The method supplies evidence of a weak ergodicity-breaking transition together with glassy dynamics in a kinetically constrained quantum model.
  • Graph measures become practical tools for locating parameter-driven ergodicity violations without requiring full diagonalization.

Where Pith is reading between the lines

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

  • The same Fock-space graph construction might be reused to track other dynamical crossovers that are hard to access at large size.
  • If the distribution signatures prove model-independent, the centrality measure could serve as a classifier for different routes to ergodicity breaking.
  • Analytical access in the thermodynamic limit opens the possibility of deriving exact scaling relations for the width or shape of the centrality distribution across the transition.

Load-bearing premise

That the Fock-space graph plus the graph-energy centrality measure together preserve the dynamical information that controls whether the system breaks ergodicity weakly.

What would settle it

In a model with an independently established weak ergodicity-breaking transition, the graph-energy centrality distribution shows no detectable change when the control parameter crosses the transition value.

Figures

Figures reproduced from arXiv: 2605.00094 by Fabian Heidrich-Meisner, Heiko Georg Menzler, Mari Carmen Ba\~nuls, Rafa{\l} \'Swi\k{e}tek.

Figure 1
Figure 1. Figure 1: Fock-space graph of the TLG model ( [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Rosenzweig-Porter model. (a),(b) Distribution of the GEC in the RPM (D = 215) for different values of γ. (c) Analytically obtained var(GEC) for the RPM as a function of γ for different Hilbert-space dimensions D. System sizes range from small ones accessible with ED to huge system sizes and we include results for the thermodynamic limit as well (D → ∞). The inset shows a zoomed-in capture of the crossing p… view at source ↗
Figure 3
Figure 3. Figure 3: Quantum Sun model. (a),(b) Distributions of the GEC in the QSM with N = 4, L = 16 for different values of α obtained from 100 realizations. (c) Variance of the GEC in the QSM across system sizes as a function of α. The variance of the GEC is obtained analytically. The inset zooms in on the crossing point around α = 1. coupled to the L localized spins through a coupling pa￾rameter g0. We label the spins ins… view at source ↗
Figure 4
Figure 4. Figure 4: Triangular lattice gas model. Diagonal ma￾trix elements of nˆL/2 for (a) V = 0.2 t0 and (b) V = 3 t0. (c) Variance of the GEC in the TLG model at half filling (N = L/2) for different system sizes as a function of V calculated using a semianalytical approach (see [84]). The inset shows the system-size dependence of the crossing point V ∗ . for V ≫ t0, the distribution of diagonal matrix elements becomes ver… view at source ↗
Figure 5
Figure 5. Figure 5: Eigenstate expectation values for the observable [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Sketch of the TLG model with particles represented as hexagons. Red arrows denote allowed hopping transitions. (b) Gap ratio ⟨rn⟩ averaged over the full spectrum of the TLG model as a function of V . The horizontal dashed line indicates the GOE value of ⟨rn⟩. (c), (d) Entanglement entropy in eigenstates as a function of their energy En for (c) V = 0.2 t0 and (d) V = 3 t0. observables that are diagonal … view at source ↗
read the original abstract

We study the onset of weak ergodicity violations in closed quantum many-body systems and focus on cases in which they occur through a transition that is controlled by a model parameter. Our analysis is based on representing quantum systems in Fock space and utilizes graph-theoretical measures. As a main result, we show that the recently introduced graph-energy centrality captures known weak ergodicity-breaking transitions via characteristic changes in its distribution. While most numerical tools are limited to small system sizes, our measure can be calculated analytically for large systems of many hundreds of sites and in some cases, even in the thermodynamic limit. We conclude by demonstrating the applicability of our Fock-space based measure to a kinetically constrained quantum model, where we find evidence for a weak ergodicity-breaking transition accompanied by glassy dynamics.

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 represents closed quantum many-body systems as graphs in Fock space and shows that the graph-energy centrality measure detects known weak ergodicity-breaking transitions through characteristic shifts in its probability distribution. The measure is claimed to be analytically tractable for systems with hundreds of sites and, in some cases, in the thermodynamic limit. The approach is demonstrated on a kinetically constrained model, where distribution changes are interpreted as evidence of a transition accompanied by glassy dynamics.

Significance. If the central claim holds, the result is significant because it supplies a scalable, graph-theoretic diagnostic for weak ergodicity breaking that bypasses the system-size limits of exact diagonalization and time evolution. The analytical accessibility for large lattices is a concrete strength, as is the explicit application to a kinetically constrained model that lies outside the usual many-body localization setting.

major comments (2)
  1. [§4] §4 (kinetically constrained model results): The central claim that distribution shifts in graph-energy centrality capture the onset of weak ergodicity breaking rests on the assumption that the static Fock-space adjacency matrix encodes the relevant dynamical constraints. In kinetically constrained models the underlying graph can remain connected while effective dynamics are confined to subspaces; the manuscript does not demonstrate that the observed centrality shift distinguishes dynamical fragmentation from generic changes in degree distribution. A direct comparison with participation ratios or long-time local observables on the same parameter sweep would be required to establish that the measure is not merely reporting connectivity changes.
  2. [§3] §3 (analytical evaluation): The assertion that the measure can be evaluated analytically for large systems and in the thermodynamic limit is load-bearing for the claimed advantage over numerical tools. The derivation of the closed-form expression for the centrality distribution (or the limiting procedure) is not shown explicitly; without it, the scalability claim cannot be assessed independently of the numerical examples.
minor comments (2)
  1. [§2] The definition of graph-energy centrality is introduced without an explicit equation number; adding a numbered equation would improve traceability when the distribution is later analyzed.
  2. [Figures] Figure captions should state the system sizes and parameter values used for each panel to allow direct comparison with the analytical limits discussed in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comments point by point below, and we will revise the manuscript accordingly to address the concerns raised.

read point-by-point responses

  1. Referee: [§4] §4 (kinetically constrained model results): The central claim that distribution shifts in graph-energy centrality captures the onset of weak ergodicity breaking rests on the assumption that the static Fock-space adjacency matrix encodes the relevant dynamical constraints. In kinetically constrained models the underlying graph can remain connected while effective dynamics are confined to subspaces; the manuscript does not demonstrate that the observed centrality shift distinguishes dynamical fragmentation from generic changes in degree distribution. A direct comparison with participation ratios or long-time local observables on the same parameter sweep would be required to establish that the measure is not merely reporting connectivity changes.

    Authors: We agree that a more explicit validation is needed to confirm that the centrality shifts reflect the dynamical constraints rather than just changes in the graph's degree distribution. In the revised manuscript, we will include a direct comparison of the graph-energy centrality distribution with participation ratios and long-time local observables across the parameter sweep for the kinetically constrained model. This will demonstrate that the shifts align with the onset of glassy dynamics and weak ergodicity breaking, rather than generic connectivity alterations. We note that the Fock-space graph is constructed from the Hamiltonian, which inherently incorporates the kinetic constraints, limiting edges to allowed transitions. revision: yes

  2. Referee: [§3] §3 (analytical evaluation): The assertion that the measure can be evaluated analytically for large systems and in the thermodynamic limit is load-bearing for the claimed advantage over numerical tools. The derivation of the closed-form expression for the centrality distribution (or the limiting procedure) is not shown explicitly; without it, the scalability claim cannot be assessed independently of the numerical examples.

    Authors: We acknowledge that the explicit derivation was omitted from the main text to maintain focus on the results. In the revised version, we will add a detailed appendix presenting the closed-form expression for the graph-energy centrality distribution and the limiting procedure to the thermodynamic limit. This will substantiate the analytical tractability for systems with hundreds of sites and beyond. revision: yes

Circularity Check

0 steps flagged

Graph-energy centrality applied to known transitions; no reduction of claims to self-definition or fitted inputs.

full rationale

The paper represents quantum systems as Fock-space graphs and applies the recently introduced graph-energy centrality measure to demonstrate characteristic distribution changes at known weak ergodicity-breaking transitions. The central result is an application and analytical extension to large systems rather than a derivation of the transitions themselves from the measure. No equations or steps reduce the claimed capture of dynamics to a tautological fit or self-citation chain; the static graph construction is independent of the dynamical signatures being observed. This is a standard non-circular use of an external measure on benchmark cases.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard assumptions from quantum many-body physics and graph theory with no free parameters or invented entities explicitly introduced in the abstract.

axioms (1)
  • domain assumption Quantum many-body systems can be faithfully represented as graphs in Fock space where nodes correspond to basis states and edges to allowed transitions under the Hamiltonian.
    This representation is the basis for applying graph-theoretical measures to detect ergodicity properties.

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Reference graph

Works this paper leans on

136 extracted references · 136 canonical work pages · 3 internal anchors

  1. [1]

    For the TLG model, GEC is calculated in the joint eigenbasis of local density operatorsˆnℓ

    is another candidate for a wEBT. For the TLG model, GEC is calculated in the joint eigenbasis of local density operatorsˆnℓ. Fig. 4(c) shows var(GEC)as a function of V for filling (N = L/2). We find a regime forV/t 0 ≲ 1where var(GEC)decreases for increasingL, while it increases forV/t 0 ≳ 1. This leads to a crossing pointV∗(L), extracted by comparing sys...

    work page

  2. [2]

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

    work page 2046

  3. [3]

    Srednicki, Chaos and quantum thermalization, Phys

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

    work page 1994

  4. [4]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2015)

    work page 2015

  5. [5]

    J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys.81, 082001 (2018)

    work page 2018

  6. [6]

    Eigenstate thermalization

    R. Patil and M. Rigol, Eigenstate thermalization (2026), arXiv:2604.11872

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  7. [7]

    Rigol, V

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

    work page 2008

  8. [8]

    Rigol, Breakdown of thermalization in finite one- dimensional systems, Phys

    M. Rigol, Breakdown of thermalization in finite one- dimensional systems, Phys. Rev. Lett.103, 100403 (2009)

    work page 2009

  9. [9]

    Rigol, Quantum quenches and thermalization in one- dimensional fermionic systems, Phys

    M. Rigol, Quantum quenches and thermalization in one- dimensional fermionic systems, Phys. Rev. A80, 053607 (2009)

    work page 2009

  10. [10]

    L. F. Santos and M. Rigol, Localization and the effects of symmetries in the thermalization properties of one- dimensional quantum systems, Phys. Rev. E82, 031130 (2010)

    work page 2010

  11. [11]

    R.Steinigeweg, J.Herbrych,andP.Prelovšek,Eigenstate thermalization within isolated spin-chain systems, Phys. Rev. E87, 012118 (2013)

    work page 2013

  12. [12]

    Khatami, G

    E. Khatami, G. Pupillo, M. Srednicki, and M. Rigol, Fluctuation-dissipation theorem in an isolated system of quantum dipolar bosons after a quench, Phys. Rev. Lett.111, 050403 (2013)

    work page 2013

  13. [13]

    S. Sorg, L. Vidmar, L. Pollet, and F. Heidrich-Meisner, Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit, Phys. Rev. A 90, 033606 (2014)

    work page 2014

  14. [14]

    Beugeling, R

    W. Beugeling, R. Moessner, and M. Haque, Finite-size scaling of eigenstate thermalization, Phys. Rev. E89, 042112 (2014)

    work page 2014

  15. [15]

    Steinigeweg, A

    R. Steinigeweg, A. Khodja, H. Niemeyer, C. Gogolin, and J. Gemmer, Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems, Phys. Rev. Lett.112, 130403 (2014)

    work page 2014

  16. [16]

    Beugeling, R

    W. Beugeling, R. Moessner, and M. Haque, Off-diagonal matrix elements of local operators in many-body quan- tum systems, Phys. Rev. E91, 012144 (2015)

    work page 2015

  17. [17]

    Mondaini, K

    R. Mondaini, K. R. Fratus, M. Srednicki, and M. Rigol, Eigenstate thermalization in the two-dimensional trans- verse field Ising model, Phys. Rev. E93, 032104 (2016)

    work page 2016

  18. [18]

    Mondaini and M

    R. Mondaini and M. Rigol, Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables, Phys. Rev. E96, 012157 (2017)

    work page 2017

  19. [19]

    Yoshizawa, E

    T. Yoshizawa, E. Iyoda, and T. Sagawa, Numerical large deviation analysis of the eigenstate thermalization hy- pothesis, Phys. Rev. Lett.120, 200604 (2018)

    work page 2018

  20. [20]

    Jansen, J

    D. Jansen, J. Stolpp, L. Vidmar, and F. Heidrich- Meisner, Eigenstate thermalization and quantum chaos in the Holstein polaron model, Phys. Rev. B99, 155130 (2019)

    work page 2019

  21. [21]

    Foini and J

    L. Foini and J. Kurchan, Eigenstate thermalization hy- pothesis and out of time order correlators, Phys. Rev. E 99, 042139 (2019)

    work page 2019

  22. [22]

    Mierzejewski and L

    M. Mierzejewski and L. Vidmar, Quantitative impact of integrals of motion on the eigenstate thermalization hypothesis, Phys. Rev. Lett.124, 040603 (2020)

    work page 2020

  23. [23]

    Richter, A

    J. Richter, A. Dymarsky, R. Steinigeweg, and J. Gemmer, Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies, Phys. Rev. E102, 042127 (2020)

    work page 2020

  24. [24]

    L. F. Santos, F. Pérez-Bernal, and E. J. Torres-Herrera, Speck of chaos, Phys. Rev. Res.2, 043034 (2020)

    work page 2020

  25. [25]

    Brenes, T

    M. Brenes, T. LeBlond, J. Goold, and M. Rigol, Eigen- state thermalization in a locally perturbed integrable system, Phys. Rev. Lett.125, 070605 (2020)

    work page 2020

  26. [26]

    Brenes, J

    M. Brenes, J. Goold, and M. Rigol, Low-frequency be- havior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain, Phys. Rev. B102, 075127 (2020)

    work page 2020

  27. [27]

    Sugimoto, R

    S. Sugimoto, R. Hamazaki, and M. Ueda, Test of the eigenstate thermalization hypothesis based on local ran- 6 dom matrix theory, Phys. Rev. Lett.126, 120602 (2021)

    work page 2021

  28. [28]

    Schönle, D

    C. Schönle, D. Jansen, F. Heidrich-Meisner, and L. Vid- mar, Eigenstate thermalization hypothesis through the lens of autocorrelation functions, Phys. Rev. B103, 235137 (2021)

    work page 2021

  29. [29]

    Pappalardi, L

    S. Pappalardi, L. Foini, and J. Kurchan, Eigenstate thermalization hypothesis and free probability, Phys. Rev. Lett.129, 170603 (2022)

    work page 2022

  30. [30]

    Pappalardi, F

    S. Pappalardi, F. Fritzsch, and T. Prosen, Full eigenstate thermalization via free cumulants in quantum lattice systems, Phys. Rev. Lett.134, 140404 (2025)

    work page 2025

  31. [31]

    Vallini, L

    E. Vallini, L. Foini, and S. Pappalardi, Refinements of the eigenstate thermalization hypothesis under lo- cal rotational invariance via free probability (2025), arXiv:2511.23217

    work page arXiv 2025

  32. [32]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys.14, 745 (2018)

    work page 2018

  33. [33]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many- body scars and weak breaking of ergodicity, Nature Physics17, 675 (2021)

    work page 2021

  34. [34]

    Desaules, K

    J.-Y. Desaules, K. Bull, A. Daniel, and Z. Papić, Hyper- grid subgraphs and the origin of scarred quantum walks in many-body Hilbert space, Phys. Rev. B105, 245137 (2022)

    work page 2022

  35. [35]

    Moudgalya and O

    S. Moudgalya and O. I. Motrunich, Exhaustive character- ization of quantum many-body scars using commutant algebras, Phys. Rev. X14, 041069 (2024)

    work page 2024

  36. [36]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: A review of exact results, Rep. Prog. Phys.85, 086501 (2022)

    work page 2022

  37. [37]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moessner, Quantum many-body scars: A quasiparticle perspective, Ann. Rev. Cond. Mat. Phys.14, 443 (2023)

    work page 2023

  38. [38]

    Evrard, A

    B. Evrard, A. Pizzi, S. I. Mistakidis, and C. B. Dag, Quantumscarsandregulareigenstatesinachaoticspinor condensate, Phys. Rev. Lett.132, 020401 (2024)

    work page 2024

  39. [39]

    Rakovszky, P

    T. Rakovszky, P. Sala, R. Verresen, M. Knap, and F. Poll- mann, Statistical localization: From strong fragmenta- tion to strong edge modes, Phys. Rev. B101, 125126 (2020)

    work page 2020

  40. [40]

    Jonay, J

    C. Jonay, J. F. Rodriguez-Nieva, and V. Khemani, Slow thermalization and subdiffusion inU (1)conserving flo- quet random circuits, Phys. Rev. B109, 024311 (2024)

    work page 2024

  41. [41]

    Zhang, Y

    L. Zhang, Y. Ke, L. Lin, and C. Lee, Floquet engineering of Hilbert space fragmentation in stark lattices, Phys. Rev. B109, 184313 (2024)

    work page 2024

  42. [42]

    F. Yang, H. Yarloo, H.-C. Zhang, K. Mølmer, and A. E. B. Nielsen, Probing Hilbert space fragmentation with strongly interacting Rydberg atoms, Phys. Rev. B 111, 144313 (2025)

    work page 2025

  43. [43]

    Aditya, Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quan- tum East models involving varying range of constraints, Phys

    S. Aditya, Diagnostics of Hilbert space fragmentation, freezing transition, and its effects in the family of quan- tum East models involving varying range of constraints, Phys. Rev. B112, 195413 (2025)

    work page 2025

  44. [44]

    Tan and Y.-P

    T.-L. Tan and Y.-P. Huang, Interference-caged quantum many-body scars: The Fock space topological localiza- tion and interference zeros (2025), arXiv:2504.07780

    work page arXiv 2025

  45. [45]

    Ben-Ami, M

    T. Ben-Ami, M. Heyl, and R. Moessner, Many-body cages: Disorder-free glassiness from flat bands in Fock space, and many-body Rabi oscillations (2025), arXiv:2504.13086

    work page arXiv 2025

  46. [46]

    Jonay and F

    C. Jonay and F. Pollmann, Localized fock space cages in kinetically constrained models, Phys. Rev. B113, 134313 (2026)

    work page 2026

  47. [47]

    Floquet Many-Body Cages

    T. Ben-Ami, R. Moessner, and M. Heyl, Floquet many- body cages (2026), arXiv:2604.13027 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  48. [48]

    Mohapatra, S

    S. Mohapatra, S. Moudgalya, and A. C. Balram, Addi- tional quantum many-body scars of the spin-1xy model with fock-space cages and commutant algebras, Phys. Rev. B113, 054310 (2026)

    work page 2026

  49. [49]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many- body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017)

    work page 2017

  50. [50]

    Kohlert, S

    T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Exploring the regime of fragmentation in strongly tilted Fermi-Hubbard chains, Phys. Rev. Lett.130, 010201 (2023)

    work page 2023

  51. [51]

    Adler, D

    D. Adler, D. Wei, M. Will, K. Srakaew, S. Agrawal, P. Weckesser, R. Moessner, F. Pollmann, I. Bloch, and J.Zeiher,ObservationofHilbertspacefragmentationand fractonic excitations in 2D, Nature636, 80–85 (2024)

    work page 2024

  52. [52]

    Karch, S

    S. Karch, S. Bandyopadhyay, Z.-H. Sun, A. Impertro, S. Huh, I. P. Rodríguez, J. F. Wienand, W. Ketterle, M. Heyl, A. Polkovnikov, I. Bloch, and M. Aidelsburger, Probing quantum many-body dynamics using subsystem Loschmidt echos (2025), arXiv:2501.16995

    work page arXiv 2025

  53. [53]

    Honda, Y

    K. Honda, Y. Takasu, S. Goto, H. Kazuta, M. Kunimi, I. Danshita, and Y. Takahashi, Observation of slow re- laxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains, Science Advances11, eadv3255 (2025)

    work page 2025

  54. [54]

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Poll- mann, Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians, Phys. Rev. X10, 011047 (2020)

    work page 2020

  55. [55]

    Khemani, M

    V. Khemani, M. Hermele, and R. Nandkishore, Local- ization from Hilbert space shattering: From theory to physical realizations, Phys. Rev. B101, 174204 (2020)

    work page 2020

  56. [56]

    Moudgalya and O

    S. Moudgalya and O. I. Motrunich, Hilbert space frag- mentation and commutant algebras, Phys. Rev. X12, 011050 (2022)

    work page 2022

  57. [57]

    Lisiecki, J

    M. Lisiecki, J. Bonča, M. Mierzejewski, J. Herbrych, and P. Łydżba, Tunable Hilbert space fragmentation and extended critical regime, Phys. Rev. B112, 195116 (2025)

    work page 2025

  58. [58]

    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

  59. [59]

    Sierant, D

    P. Sierant, D. Delande, and J. Zakrzewski, Many-body localization due to random interactions, Phys. Rev. A 95, 021601 (2017)

    work page 2017

  60. [60]

    Khemani, D

    V. Khemani, D. N. Sheng, and D. A. Huse, Two univer- sality classes for the many-body localization transition, Phys. Rev. Lett.119, 075702 (2017)

    work page 2017

  61. [61]

    R. K. Panda, A. Scardicchio, M. Schulz, S. R. Taylor, and M. Žnidarič, Can we study the many-body localisation transition?, EPL128, 67003 (2019)

    work page 2019

  62. [62]

    D. E. Logan and S. Welsh, Many-body localization in Fock space: A local perspective, Phys. Rev. B99, 045131 (2019)

    work page 2019

  63. [63]

    L. A. Colmenarez, P. A. McClarty, M. Haque, and D. J. Luitz, Statistics of correlation functions in the random 7 Heisenberg chain, SciPost Physics7, 064 (2019)

    work page 2019

  64. [64]

    Á. L. Corps, R. A. Molina, and A. Relaño, Signatures of a critical point in the many-body localization transition, SciPost Phys.10, 107 (2021)

    work page 2021

  65. [65]

    Abanin, J

    D. Abanin, J. Bardarson, G. De Tomasi, S. Gopalakr- ishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Ann. Phys.427, 168415 (2021)

    work page 2021

  66. [66]

    Prakash, J

    A. Prakash, J. H. Pixley, and M. Kulkarni, Universal spectral form factor for many-body localization, Phys. Rev. Research3, L012019 (2021)

    work page 2021

  67. [67]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Zakrzewski, Many-body localization in the age of classical computing, Rep. Prog. Phys.88, 026502 (2025)

    work page 2025

  68. [69]

    A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Transition from localized to ex- tended eigenstates in the ensemble of power-law random banded matrices, Phys. Rev. E54, 3221 (1996)

    work page 1996

  69. [70]

    A. D. Mirlin and F. Evers, Multifractality and critical fluctuations at the anderson transition, Phys. Rev. B62, 7920 (2000)

    work page 2000

  70. [71]

    Evers and A

    F. Evers and A. D. Mirlin, Fluctuations of the inverse participation ratio at the anderson transition, Phys. Rev. Lett.84, 3690 (2000)

    work page 2000

  71. [73]

    Bogomolny and M

    E. Bogomolny and M. Sieber, Power-law random banded matrices and ultrametric matrices: Eigenvector distribu- tion in the intermediate regime, Phys. Rev. E98, 042116 (2018)

    work page 2018

  72. [75]

    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

  73. [76]

    Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath

    K. Pawlik, N. Laflorencie, and J. Zakrzewski, Uncon- ventional thermalization of a localized chain interacting with an ergodic bath (2026), arXiv:2507.18286 [cond- mat.dis-nn]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  74. [79]

    Świętek, M

    R. Świętek, M. Hopjan, C. Vanoni, A. Scardicchio, and L. Vidmar, Scaling theory of fading ergodicity, Phys. Rev. Lett.135, 170401 (2025)

    work page 2025

  75. [80]

    Świętek, M

    R. Świętek, M. Kliczkowski, M. Hopjan, and L. Vidmar, Fading ergodicity and quantum dynamics in random matrix ensembles (2026), arXiv:2603.23616

    work page arXiv 2026

  76. [81]

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

    work page 2013

  77. [82]

    Deger and A

    A. Deger and A. Lazarides, Weak ergodicity breaking transition in a randomly constrained model, Phys. Rev. B109, L220301 (2024)

    work page 2024

  78. [83]

    Roy and A

    S. Roy and A. Lazarides, Strong ergodicity breaking due to local constraints in a quantum system, Phys. Rev. Res.2, 023159 (2020)

    work page 2020

  79. [85]

    Z. Lan, M. van Horssen, S. Powell, and J. P. Garra- han, Quantum slow relaxation and metastability due to dynamical constraints, Phys. Rev. Lett.121, 040603 (2018)

    work page 2018

  80. [86]

    Royen, S

    K. Royen, S. Mondal, F. Pollmann, and F. Heidrich- Meisner, Enhanced many-body localization in a kinet- ically constrained model, Phys. Rev. E109, 024136 (2024)

    work page 2024

Showing first 80 references.