Pith. sign in

REVIEW 3 major objections 3 minor 164 references

In a flavor-extended Z2 lattice gauge theory, binary disorder only produces a long-lived non-ergodic transient, whereas multilevel disorder yields many-body-localization-like behavior.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 00:37 UTC pith:ZPN3DSDF

load-bearing objection Sharp, multi-diagnostic separation of binary from multilevel disorder in DFL; n≥4 thermodynamic-limit claim rests on an acknowledged empirical χ-collapse, but the core result holds up. the 3 major comments →

arxiv 2607.26156 v1 pith:ZPN3DSDF submitted 2026-07-28 quant-ph cond-mat.quant-gascond-mat.stat-mechcond-mat.str-elhep-lat

Role of flavor degrees of freedom in quantum simulations of disorder-free localization

Yizhuo Tian , Jared Jeyaretnam , Tanmay Bhore , Zlatko Papi\'c , Jad C. Halimeh This is my paper
classification quant-ph cond-mat.quant-gascond-mat.stat-mechcond-mat.str-elhep-lat
keywords disorder-free localizationmany-body localizationlattice gauge theoryHilbert-space fragmentationspectral towerslevel statisticsentanglement spectruminfinite matrix product states
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.

This paper asks what spectrum of conserved local variables is needed to produce robust many-body localization (MBL) in a disorder-free lattice gauge theory. It shows that binary (two-level) bond disorder, despite having the largest variance, produces only a long-lived non-ergodic transient: finite-size and finite-time diagnostics look localized, but eigenstate entanglement retains a volume-law contribution, level statistics remain closer to random-matrix, and the dynamics eventually relax. Multilevel disorder (four or eight levels) instead yields consistent MBL-like signatures — Poissonian level statistics, area-law eigenstate entanglement, nonthermal entanglement spectra, and persistent local memory in thermodynamic-limit simulations. The mechanism is the local spectrum: binary disorder has one bond magnitude, generating degenerate spectral towers and approximate Hilbert-space fragmentation, whereas multilevel disorder has several local excitation energies that lift degeneracies and suppress resonances. If correct, this means conserved 'flavor' degrees of freedom do not generically produce localization; their number of levels is a design parameter.

Core claim

The paper's central claim is that in a Z2 lattice gauge theory with static flavor degrees of freedom — which maps onto a mixed-field Ising chain with n-level bond disorder — the localization properties depend qualitatively on n. For n=2, the apparent localization at finite sizes and intermediate times ultimately gives way to thermalization; the slow dynamics arises from energy-scale separation, degenerate spectral towers, and approximate Hilbert-space fragmentation. For n=4 and n=8, the system exhibits mutually consistent MBL-like signatures, including Poissonian level statistics, area-law eigenstate entanglement, nonthermal entanglement spectra, and persistent local memory over accessible t

What carries the argument

The central object is the flavored gauge theory of Eq. (1), where each link is augmented by an n-level 'flavor' degree of freedom D^(n)_j whose eigenvalues are equally spaced between −1 and +1. Gauge fixing and elimination of matter map the model to a mixed-field Ising chain with n-level bond disorder g^(n)_j = ± D^(n)_j, Eq. (6). Because the flavor variables are conserved, an equal superposition of their eigenstates implements the disorder average in a single translationally-invariant evolution. The paper uses exact diagonalization (level statistics, eigenstate entanglement, participation ratios, entanglement spectra) and infinite matrix-product-state dynamics (iTDVP) to compare n=2, 4, 8,

Load-bearing premise

The claim that multilevel disorder localizes in the thermodynamic limit rests on the assumption that the late-time decay seen in finite-bond-dimension iMPS data is a truncation artifact; this is supported by an empirical scaling collapse of the decay time with a power of the bond dimension, but the exponents are fitted post hoc and not derived from the dynamics.

What would settle it

A concrete falsifier: for n=4 at strong coupling, repeat the infinite-matrix-product-state simulation with larger bond dimension and check whether the decay time of the local-memory plateau continues to grow as a power of the bond dimension (χ^{3/4}). If instead the decay time saturates, the plateau is a truncation artifact and the MBL-like claim fails. For n=2, a falsifier would be observing a nonthermal plateau that survives for times growing with system size, indicating genuine localization rather than a transient.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, quantum simulators using two-level ancillas to encode disorder should expect only a prethermal plateau, not genuine localization; going from one to two ancillary qubits per site changes the physics qualitatively.
  • The disorder variance is not the controlling parameter: binary disorder has the largest RMS coupling yet the weakest localization, so protocols should be designed around the local spectrum rather than matching variances.
  • Multilevel disorder in this model provides a clean setting to study MBL without external quenched disorder, including in the thermodynamic limit via quantum parallelism.
  • The distinction between fragmentation-induced slow dynamics and true MBL can be diagnosed by eigenstate entanglement scaling and participation ratios, not just time-dependent observables.
  • The mapping from bond to site disorder for n=2 shows that binary bond disorder is exactly equivalent to binary site disorder, so the binary phenomenology applies to random-field chains with two-level fields.

Where Pith is reading between the lines

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

  • A direct test of the paper's mechanism would be to vary the level spacing or the weights of the flavor distribution: the theory predicts that localization should depend on the set of local excitation energies, not simply on n or the variance.
  • One might expect the n=2 transient to be exponentially long in the disorder strength, since the tower spacing sets the energy-scale separation; this could be probed by measuring the relaxation time as a function of µ and h.
  • The scaling collapse of the finite-bond-dimension decay time with χ^{3/4} and χ^{1/2} is an empirical fit; if a future simulation with larger bond dimension or a different algorithm shows a collapse with a different exponent, the conclusion that the plateau persists would be strengthened or weakened.
  • The framework suggests that non-flavor static conserved variables with more than two levels, such as higher-spin degrees of freedom, could be used to engineer robust disorder-free localization in experiments.

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

3 major / 3 minor

Summary. The paper studies a one-dimensional Z2 lattice gauge theory augmented by static n-level flavor degrees of freedom. After gauge fixing and eliminating matter fields, the model maps onto a mixed-field Ising chain with n-level bond disorder, where different flavor configurations act as disorder realizations. Using exact diagonalization (level statistics, eigenstate entanglement entropy and entanglement spectrum, participation ratios, quench dynamics) and infinite-matrix-product-state time-dependent variational principle (iMPS/iTDVP) dynamics directly in the thermodynamic limit, the authors compare n=2, 4, 8, and continuous disorder. They argue that binary (n=2) bond disorder produces only a long-lived non-ergodic transient arising from degenerate spectral towers and approximate Hilbert-space fragmentation, ultimately thermalizing, whereas n>=4 bond disorder yields mutually consistent MBL-like signatures: Poissonian level statistics, area-law eigenstate entanglement, nonthermal entanglement spectra, localization in the x-basis, and persistent local memory over accessible thermodynamic-limit times. The central claim is that localization is governed not by the disorder variance but by the local disorder spectrum and the resulting resonant connectivity of the many-body Hilbert space.

Significance. If the central claim holds, this is a timely and non-obvious result for disorder-free localization and quantum simulation of disordered systems: not all discrete disorder distributions behave alike, and binary disorder can masquerade as MBL while actually being a prethermal/fragmentation transient. The paper provides multiple independent diagnostics, derives the LGT-to-Ising mapping explicitly, and uses a thermodynamic-limit iMPS method with the disorder ensemble encoded in ancillary degrees of freedom. The negative claim for n=2 is relatively robust because its relaxation is converged in the accessible iMPS window. However, the positive claim for n>=4 ultimately depends on an empirical finite-bond-dimension extrapolation, which is the main weakness and needs to be addressed before the strong conclusions can be fully endorsed.

major comments (3)
  1. [Sec. V / Fig. 9, and Conclusions] The central positive claim that n=4 and n=8 retain local memory in the thermodynamic limit rests on the empirical scaling collapse of the finite-χ decay time, τ ∝ χ^{3/4} (n=4) and τ ∝ χ^{1/2} (n=8), shown in Fig. 9. These exponents are fitted post hoc, no mechanism is given for why truncation produces these particular powers, and the collapse is displayed only for C_XX(t), not for the staggered magnetization M(t). If the true χ→∞ dynamics relaxes on a finite timescale, the plateau is a truncation artifact and the MBL-like classification would collapse. The finite-size ED data in Appendix G (N=14) cannot settle this. I request either a theoretical justification of the χ-scaling, a collapse of both observables and larger-χ data, or a clear softening of the claim to "long-lived prethermal plateau on accessible scales." The current language — "persistent local memory over accessible times i
  2. [Sec. III / Fig. 2] The level-statistics comparison is made at a single system size (N=16). The values of ⟨r⟩ for n=2 and n≥4 are both suppressed in broad regions of the (h, μ) plane; the distinction between the two cases is carried by the entanglement scaling in Fig. 3, not by ⟨r⟩ itself. To support "Poissonian level statistics" as an MBL signature and to exclude the alternative that the suppressed r is a finite-size/fragmentation effect, a finite-size scaling analysis of ⟨r⟩ (e.g., N=10,12,14,16) in the same parameter regions should be provided, or the claim should be qualified. Without this, the level-statistics diagnostic is consistent with both the MBL and the prethermal/fragmentation scenarios.
  3. [Sec. IV] The mechanism for the slow n=2 dynamics — "approximate Hilbert-space fragmentation" — is presented qualitatively. The spectral towers and the participation-ratio growth (Fig. 10) are consistent with this picture, but no quantitative measure of fragmentation (e.g., dimensions of the largest invariant subspaces, or a Mazur-bound estimate) is provided. Since this mechanism is load-bearing for explaining why binary disorder thermalizes only after a long transient, a quantitative proxy would considerably strengthen the argument.
minor comments (3)
  1. [Fig. 9] The scaling collapse in the main panels is shown only for C_XX(t). If both observables are claimed to collapse, the corresponding M(t) collapse should be shown (e.g., as a supplementary panel); otherwise the text should state explicitly that only C_XX is collapsed.
  2. [Appendix F] The procedure for estimating the uncertainty in the 1/χ extrapolation is not described. Please specify how the shaded bands in Fig. 7 were computed (e.g., standard error of the fit, jackknife, or spread among extrapolation windows).
  3. [Appendix G / Fig. 14] The text describes "sub-ballistic entanglement-entropy growth" for n=4,8 at large μ, but the fits shown are linear-in-time (n=2) and logarithmic-in-time (n=4,8). Consider using "sublinear" or "logarithmic" for precision.

Circularity Check

0 steps flagged

No definitional circularity; the central n=2 vs n>=4 distinction is independently derived and benchmarked, with only minor non-load-bearing self-citations.

full rationale

Walking the derivation chain: (i) Eq. (1) defines the flavor-extended Z2 LGT, and Appendix A derives the mapping to the mixed-field Ising chain with n-level bond disorder, Eq. (6), via an explicit unitary transformation that fixes Gauss's law. This is an algebraic equivalence and does not assume the localization conclusion. (ii) The disorder average via flavor ancillas, Eqs. (5)-(7), is exact because [H0, D_j^(n)] = 0, so the ensemble average is not a fitted input. (iii) The n=2 spectral-tower mechanism is derived in Sec. IV A from Eq. (12)-(13): equal bond magnitudes imply E = E_GS + 2µ N_d with degeneracy 2*binom(N-1,N_d). The bond-to-site mapping in Appendix C is also an exact unitary transformation. The same-authors citation [147] is used for the interpretive label 'approximate Hilbert-space fragmentation and slow dynamics', but the slow dynamics is directly demonstrated by the paper's own ED and iTDVP data, so the citation is not load-bearing. (iv) The n>=4 MBL-like classification rests on mutually consistent diagnostics: level statistics (Fig. 2), eigenstate entanglement scaling (Fig. 3), entanglement spectra (Figs. 6, 11), participation ratios (Fig. 10), and iTDVP plateaus (Figs. 7-9). The only fitted quantities are diagnostic extrapolations, namely the volume-law coefficient s_V in Eq. (10) and the χ-collapse exponents in Fig. 9. The paper explicitly labels the latter as empirical: 'the curves collapse approximately when time is rescaled as t/χ^{3/4} for n=4, and t/χ^{1/2} for n=8', and 'Extrapolating this empirical scaling suggests...'. It also explicitly disclaims asymptotic localization: 'Our results do not establish the asymptotic stability of MBL for n=4 or n=8' and 'Although the accessible times do not establish asymptotic localization'. Thus no central claim is equivalent by construction to its inputs; the χ→∞ extrapolation is a numerical robustness concern, not circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The central claim rests on the exactness of the LGT-to-Ising mapping (App. A), the choice of uniform disorder ensemble, and the validity of the iMPS disorder-averaging and MBL diagnostics. The only genuinely fitted numbers are diagnostic: the χ-collapse exponents and the entropy-scaling parameters; neither defines the outcome by construction. The flavor variables are model inputs, not invented entities - they are experimentally realizable ancillas, not entities inserted to explain the result.

free parameters (2)
  • χ-collapse exponents = 3/4 (n=4), 1/2 (n=8)
    Chosen by fitting the late-time decay curves in Fig. 9 onto a single collapsed curve; these exponents govern the extrapolation that converts truncation-induced decay into 'persistent memory in the thermodynamic limit.' They are diagnostic, not part of the model Hamiltonian, but the thermodynamic-limit claim leans on them.
  • Volume-law fit parameters (s_V, c) = fitted per curve to ⟨S_E(N)⟩ = s_V N/2 + c, N=8..16
    The area-law/volume-law classification in Fig. 3 is read off from this two-parameter fit over small system sizes; a different fitting window or additional data could change the inferred s_V.
axioms (5)
  • standard math The Appendix A gauge-fixing/matter-elimination mapping from the Z2 LGT (Eq. 1) to the mixed-field Ising chain (Eqs. 5-6) is exact and preserves all relevant spectral and dynamical properties.
    Invoked in Sec. II and App. A; the entire study is conducted on the mapped model.
  • domain assumption A uniform weighting of the n flavor eigenvalues (Eq. 7) is the relevant disorder ensemble for reproducing DFL and the Google experiment.
    The equal-superposition initial state implements the uniform disorder average; the paper leaves non-uniform flavor weights to future work (Sec. VI).
  • domain assumption The iMPS evolution with a four-site unit cell and flavor ancillas correctly reproduces the disorder-averaged dynamics in the thermodynamic limit.
    Used in Sec. V; relies on configurations not mixing and on bond dimension χ up to 400 capturing all relevant correlations. The paper identifies truncation as a controlled error source (App. F).
  • domain assumption Standard MBL diagnostics (Poissonian ⟨r⟩, area-law S_E, non-thermal entanglement spectrum, persistent local memory) jointly indicate localization at accessible sizes/times.
    Invoked throughout Secs. III-V; the paper itself notes these do not establish asymptotic MBL (Sec. VI).
  • standard math Marchenko-Pastur is the correct finite-dimension reference for thermal entanglement spectra.
    Used in Sec. III/E to define D_KL; follows from random-matrix theory (Refs. 150-151).

pith-pipeline@v1.3.0-alltime-deepseek · 30918 in / 13576 out tokens · 132926 ms · 2026-08-01T00:37:29.262444+00:00 · methodology

0 comments
read the original abstract

A recent \texttt{Google Quantum AI} experiment [\href{https://www.science.org/doi/10.1126/science.adr9680}{Gyawali \textit{et al.}, Science \textbf{393}, 71 (2026)}] has exploited quantum parallelism to emulate disorder-averaged many-body dynamics, with conserved local degrees of freedom generating an effective disorder potential. We investigate how the local spectrum of these static variables controls localization in a flavor-extended ${\mathbb Z}_2$ lattice gauge theory, which maps onto a mixed-field Ising chain with $n$-level bond disorder. Combining finite-size spectral and entanglement diagnostics with infinite matrix-product state dynamics, we find a qualitative distinction between binary and multilevel disorder. For $n=2$, apparent localization ultimately gives way to thermalization; the long-lived transient arises from energy-scale separation, degenerate spectral towers, and approximate Hilbert-space fragmentation. By contrast, $n=4$ displays consistent localization signatures, including Poissonian level statistics, area-law eigenstate entanglement, nonthermal entanglement spectra, and persistent local memory over accessible times in the thermodynamic limit. Our results show that, despite its larger variance, binary disorder lacks the local amplitude diversity needed to suppress resonances. Thus, localization is governed not simply by disorder strength, but by the local disorder spectrum and the resulting resonant connectivity of the many-body Hilbert space.

Figures

Figures reproduced from arXiv: 2607.26156 by Jad C. Halimeh, Jared Jeyaretnam, Tanmay Bhore, Yizhuo Tian, Zlatko Papi\'c.

Figure 1
Figure 1. Figure 1: (a) Schematic of a Z2 lattice gauge theory and its mapping to an effective spin chain with n-level bond disorder. Top: Z2 gauge fields coupled to matter, with static external “flavor” particles coupled to the matter. Middle: After gauge fixing and eliminating matter fields (see Appendix A), the model maps to a mixed-field Ising chain with disordered couplings gj , whose signs and magnitudes are set by the … view at source ↗
Figure 2
Figure 2. Figure 2: Mean level-spacing ratio ⟨r⟩ as a function of the lon￾gitudinal field h and effective disorder scale µ, for the model in Eq. (6) at system size N = 16 and different numbers n of discrete disorder levels. Here, n = ∞ in panel (d) denotes a continuous uniform distribution g ∈ [−1, 1]. Results are av￾eraged over 300 disorder realizations and the 100 eigenstates closest to the peak of the density of states. Th… view at source ↗
Figure 3
Figure 3. Figure 3: Finite-size scaling of the bipartite entanglement entropy in many-body eigenstates of the model in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Disorder-averaged density of states P(E) for N = 12 and the indicated values of n. (a) Thermal regime, (h, µ) = (0.5, 1.5). (b) Strong-coupling regime, (h, µ) = (0.5, 8). For finite n, the spectrum organizes into structures separated by multiples of 2µ/(n−1); these are most pronounced for binary disorder. (c) Strong-field regime, (h, µ) = (6, 1.5), where the principal towers are separated by 2h. (d) Magnif… view at source ↗
Figure 5
Figure 5. Figure 5: Bipartite entanglement entropy SE/ ln 2 of every eigenstate as a function of energy for N = 12. Columns correspond to n = 2, 4,∞, while rows show (h, µ) = (0.5, 1.5), (0.5, 8), and (6, 1.5). Color denotes the local density of points, and the accompanying histograms show the distribution of SE. Binary disorder retains broad distributions of entangled eigenstates in the strong-coupling and strong-field regim… view at source ↗
Figure 6
Figure 6. Figure 6: Entanglement spectra for midspectrum eigen [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Dynamics obtained by iTDVP for varying numbers of disorder levels [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Dynamics obtained by iTDVP for varying numbers of disorder levels [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: iTDVP simulations at the point µ = 5.5, h = 0.5, J = 1.0, for varying bond dimension χ, for n = 4, 8. The early-time dynamics (before J t ≃ 10) is converged in bond dimension, as shown in the insets, and we observe a clear plateau in magnetization M(t) and nearest-neighbor corre￾lation CXX. However, at later times, the traces diverge, with magnetization and correlations decaying to zero, on a timescale inc… view at source ↗
Figure 10
Figure 10. Figure 10: Participation ratio (PR) of mid-spectrum eigen [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: The long-time dynamics simulated via exact diagonalization with system size [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of the entanglement growth for [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

164 extracted references · 15 linked inside Pith

  1. [1]

    Polkovnikov, K

    A. Polkovnikov, K. Sengupta, A. Silva, and M. Ven- galattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011)

    2011

  2. [2]

    Eisert, M

    J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- body systems out of equilibrium, Nat. Phys.11, 124 (2015)

    2015

  3. [3]

    The key difference is thatn= 2 randomizes only the signs of the bonds while leaving all magnitudes identical

    Therefore, bi- nary disorder has the largest root-mean-square coupling, yet exhibits the weakest evidence of localization. The key difference is thatn= 2 randomizes only the signs of the bonds while leaving all magnitudes identical. Con- sequently, every bond defect has the same elementary energy cost, preserving extensively degenerate spectral 12 towers ...

    2024

  4. [4]

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

    2046

  5. [5]

    Srednicki, Chaos and quantum thermalization, Phys

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

    1994

  6. [6]

    Rigol, V

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

    2008

  7. [7]

    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 (2016)

    2016

  8. [8]

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

    2018

  9. [9]

    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. Vuleti´ c, and M. D. Lukin, Probing many- body dynamics on a 51-atom quantum simulator, Na- ture551, 579 (2017)

    2017

  10. [10]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Ser- byn, and Z. Papi´ c, Weak ergodicity breaking from quan- tum many-body scars, Nat. Phys.14, 745 (2018)

    2018

  11. [11]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papi´ c, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys.17, 675 (2021)

    2021

  12. [12]

    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 18 (2022)

    2022

  13. [13]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moess- ner, Quantum many-body scars: A quasiparticle per- spective, Annu. Rev. Condens. Matter Phys.14, 443 (2023)

    2023

  14. [14]

    I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interact- ing Electrons in Disordered Wires: Anderson Localiza- tion and Low-TTransport, Phys. Rev. Lett.95, 206603 (2005)

    2005

  15. [15]

    Basko, I

    D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states, Ann. Phys. (NY) 321, 1126 (2006)

    2006

  16. [16]

    Pal and D

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

    2010

  17. [17]

    Serbyn, Z

    M. Serbyn, Z. Papi´ c, and D. A. Abanin, Local Conser- vation Laws and the Structure of the Many-Body Lo- calized States, Phys. Rev. Lett.111, 127201 (2013)

    2013

  18. [18]

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

    2014

  19. [19]

    V. Ros, M. M¨ uller, and A. Scardicchio, Integrals of mo- tion in the many-body localized phase, Nucl. Phys. B 891, 420 (2015)

    2015

  20. [20]

    J. Z. Imbrie, Diagonalization and Many-Body Localiza- tion for a Disordered Quantum Spin Chain, Phys. Rev. Lett.117, 027201 (2016)

    2016

  21. [21]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-Body Localiza- tion and Thermalization in Quantum Statistical Me- chanics, Annu. Rev. Condens. Matter Phys.6, 15 (2015)

    2015

  22. [22]

    D. A. Abanin and Z. Papi´ c, Recent progress in many- body localization, Ann. Phys.529, 1700169 (2017)

    2017

  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]

    Alet and N

    F. Alet and N. Laflorencie, Many-body localization: An introduction and selected topics, C.R. Phys.19, 498 (2018)

    2018

  25. [25]

    De Roeck and F

    W. De Roeck and F. Huveneers, Stability and insta- bility towards delocalization in many-body localization systems, Phys. Rev. B95, 155129 (2017)

    2017

  26. [26]

    Herviou, S

    L. Herviou, S. Bera, and J. H. Bardarson, Multiscale en- tanglement clusters at the many-body localization phase transition, Phys. Rev. B99, 134205 (2019)

    2019

  27. [27]

    Gopalakrishnan and D

    S. Gopalakrishnan and D. A. Huse, Instability of Many- Body Localized Systems as a Phase Transition in a Nonstandard Thermodynamic Limit, Phys. Rev. B99, 134305 (2019)

    2019

  28. [28]

    ˇSuntajs, J

    J. ˇSuntajs, J. Bonˇ ca, T. Prosen, and L. Vidmar, Quan- tum chaos challenges many-body localization, Phys. Rev. E102, 062144 (2020)

    2020

  29. [29]

    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 sys- tems, Ann. Phys.427, 168415 (2021)

    2021

  30. [30]

    P. J. D. Crowley and A. Chandran, A constructive the- ory of the numerically accessible many-body localized to thermal crossover, SciPost Phys.12, 201 (2022)

    2022

  31. [31]

    Colmenarez, D

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

    2024

  32. [32]

    Sels and A

    D. Sels and A. Polkovnikov, Thermalization of Dilute Impurities in One-Dimensional Spin Chains, Phys. Rev. X13, 011041 (2023)

    2023

  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]

    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 local- ized system, Nat. Phys.19, 481 (2023)

    2023

  35. [35]

    H. Ha, A. Morningstar, and D. A. Huse, Many-Body Resonances in the Avalanche Instability of Many-Body Localization, Phys. Rev. Lett.130, 250405 (2023)

    2023

  36. [36]

    Biroli, A

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

    2024

  37. [37]

    Laflorencie, J

    N. Laflorencie, J. Colbois, and F. Alet, Cat states carry- ing long-range correlations in the many-body localized phase, Phys. Rev. B112, 224207 (2025)

    2025

  38. [38]

    Padhan, J

    A. Padhan, J. Colbois, F. Alet, and N. Laflorencie, Long-Range Resonances in Quasiperiodic Many-Body Localization, Phys. Rev. Lett.136, 197101 (2026)

    2026

  39. [39]

    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)

    2025

  40. [40]

    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

  41. [41]

    yoon Choi, S

    J. yoon 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

  42. [42]

    Bordia, H

    P. Bordia, H. P. L¨ uschen, S. S. Hodgman, M. Schreiber, I. Bloch, and U. Schneider, Coupling Identical one- dimensional Many-Body Localized Systems, Phys. Rev. Lett.116, 140401 (2016)

    2016

  43. [43]

    Smith, A

    J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Mon- roe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys.12, 907 (2016)

    2016

  44. [44]

    Roushan, C

    P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Fowler, B. Foxen, M. Giustina, E. Jeffrey, J. Kelly, E. Lucero, J. Mutus, M. Nee- ley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. White, H. Neven, D. G. Angelakis, and J. Martinis, Spectroscopic signatures of localization ...

    2017

  45. [45]

    Rispoli, A

    M. Rispoli, A. Lukin, R. Schittko, S. Kim, M. E. Tai, J. L´ eonard, and M. Greiner, Quantum critical behaviour at the many-body localization transition, Nature573, 385 (2019)

    2019

  46. [46]

    Lukin, M

    A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, S. Choi, V. Khemani, J. L´ eonard, and M. Greiner, Probing entanglement in a many- body–localized system, Science364, 256 (2019)

    2019

  47. [47]

    Y. Yao, L. Xiang, Z. Guo, Z. Bao, Y.-F. Yang, Z. Song, H. Shi, X. Zhu, F. Jin, J. Chen, S. Xu, Z. Zhu, F. Shen, 19 N. Wang, C. Zhang, Y. Wu, Y. Zou, P. Zhang, H. Li, Z. Wang, C. Song, C. Cheng, R. Mondaini, H. Wang, J. Q. You, S.-Y. Zhu, L. Ying, and Q. Guo, Observation of many-body Fock space dynamics in two dimensions, Nat. Phys.19, 1459 (2023)

    2023

  48. [48]

    L. J. Stanley, P. V. Lin, J. Jaroszy´ nski, and D. Popovi´ c, Screening the Coulomb interaction leads to a prethermal regime in two-dimensional bad conductors, Nat. Com- mun.14, 7004 (2023)

    2023

  49. [49]

    J. A. Kj¨ all, J. H. Bardarson, and F. Pollmann, Many- Body Localization in a Disordered Quantum Ising Chain, Phys. Rev. Lett.113, 107204 (2014)

    2014

  50. [50]

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

    2015

  51. [51]

    Bar Lev, G

    Y. Bar Lev, G. Cohen, and D. R. Reichman, Absence of Diffusion in an Interacting System of Spinless Fermions on a One-Dimensional Disordered Lattice, Phys. Rev. Lett.114, 100601 (2015)

    2015

  52. [52]

    Mondaini and M

    R. Mondaini and M. Rigol, Many-body localization and thermalization in disordered Hubbard chains, Phys. Rev. A92, 041601 (2015)

    2015

  53. [53]

    T. E. O’Brien, D. A. Abanin, G. Vidal, and Z. Papi´ c, Explicit construction of local conserved operators in dis- ordered many-body systems, Phys. Rev. B94, 144208 (2016)

    2016

  54. [54]

    J. Gray, S. Bose, and A. Bayat, Many-body localiza- tion transition: Schmidt gap, entanglement length, and scaling, Phys. Rev. B97, 201105 (2018)

    2018

  55. [55]

    Mierzejewski, M

    M. Mierzejewski, M. Kozarzewski, and P. Prelovˇ sek, Counting local integrals of motion in disordered spinless-fermion and Hubbard chains, Phys. Rev. B97, 064204 (2018)

    2018

  56. [56]

    Th´ eveniaut, Z

    H. Th´ eveniaut, Z. Lan, G. Meyer, and F. Alet, Tran- sition to a many-body localized regime in a two- dimensional disordered quantum dimer model, Phys. Rev. Res.2, 033154 (2020)

    2020

  57. [57]

    Pietracaprina and F

    F. Pietracaprina and F. Alet, Probing many-body lo- calization in a disordered quantum dimer model on the honeycomb lattice, SciPost Phys.10, 044 (2021)

    2021

  58. [58]

    Jeyaretnam, C

    J. Jeyaretnam, C. J. Turner, and A. Pal, Renormal- ization view on resonance proliferation between many- body localized phases, Phys. Rev. B108, 094205 (2023)

    2023

  59. [59]

    Paredes, F

    B. Paredes, F. Verstraete, and J. I. Cirac, Exploit- ing Quantum Parallelism to Simulate Quantum Ran- dom Many-Body Systems, Phys. Rev. Lett.95, 140501 (2005)

    2005

  60. [60]

    T. Enss, F. Andraschko, and J. Sirker, Many-body lo- calization in infinite chains, Phys. Rev. B95, 045121 (2017)

    2017

  61. [61]

    K. G. Wilson, Confinement of quarks, Phys. Rev. D10, 2445 (1974)

    1974

  62. [62]

    Kogut and L

    J. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D11, 395 (1975)

    1975

  63. [63]

    Montvay and G

    I. Montvay and G. M¨ unster,Quantum fields on a lattice (Cambridge University Press, 1994)

    1994

  64. [64]

    H. J. Rothe,Lattice Gauge Theories: An Introduction (Fourth Edition)(World Scientific Publishing Company, 2012)

    2012

  65. [65]

    Smith, J

    A. Smith, J. Knolle, R. Moessner, and D. L. Kovrizhin, Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Lo- calization, Phys. Rev. Lett.119, 176601 (2017)

    2017

  66. [66]

    Smith, J

    A. Smith, J. Knolle, D. L. Kovrizhin, and R. Moess- ner, Disorder-Free Localization, Phys. Rev. Lett.118, 266601 (2017)

    2017

  67. [67]

    R. M. Nandkishore and S. L. Sondhi, Many-Body Lo- calization with Long-Range Interactions, Phys. Rev. X 7, 041021 (2017)

    2017

  68. [68]

    Metavitsiadis, A

    A. Metavitsiadis, A. Pidatella, and W. Brenig, Ther- mal transport in a two-dimensionalZ 2 spin liquid, Phys. Rev. B96, 205121 (2017)

    2017

  69. [69]

    A. A. Akhtar, R. M. Nandkishore, and S. L. Sondhi, Symmetry breaking and localization in a random Schwinger model with commensuration, Phys. Rev. B 98, 115109 (2018)

    2018

  70. [70]

    Papaefstathiou, A

    I. Papaefstathiou, A. Smith, and J. Knolle, Disorder- free localization in a simpleU(1) lattice gauge theory, Phys. Rev. B102, 165132 (2020)

    2020

  71. [71]

    Brenes, M

    M. Brenes, M. Dalmonte, M. Heyl, and A. Scardicchio, Many-Body Localization Dynamics from Gauge Invari- ance, Phys. Rev. Lett.120, 030601 (2018)

    2018

  72. [72]

    Chanda, J

    T. Chanda, J. Zakrzewski, M. Lewenstein, and L. Tagli- acozzo, Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model, Phys. Rev. Lett.124, 180602 (2020)

    2020

  73. [73]

    P. A. McClarty, M. Haque, A. Sen, and J. Richter, Disorder-free localization and many-body quantum scars from magnetic frustration, Phys. Rev. B102, 224303 (2020)

    2020

  74. [74]

    O. Hart, S. Gopalakrishnan, and C. Castelnovo, Loga- rithmic Entanglement Growth from Disorder-Free Lo- calization in the Two-Leg Compass Ladder, Phys. Rev. Lett.126, 227202 (2021)

    2021

  75. [75]

    Zhu and M

    G.-Y. Zhu and M. Heyl, Subdiffusive dynamics and crit- ical quantum correlations in a disorder-free localized Ki- taev honeycomb model out of equilibrium, Phys. Rev. Res.3, L032069 (2021)

    2021

  76. [76]

    Karpov, R

    P. Karpov, R. Verdel, Y.-P. Huang, M. Schmitt, and M. Heyl, Disorder-Free Localization in an Interacting 2D Lattice Gauge Theory, Phys. Rev. Lett.126, 130401 (2021)

    2021

  77. [77]

    J. Sous, B. Kloss, D. M. Kennes, D. R. Reichman, and A. J. Millis, Phonon-induced disorder in dynamics of op- tically pumped metals from nonlinear electron-phonon coupling, Nat. Commun.12, 5803 (2021)

    2021

  78. [78]

    J. C. Halimeh, L. Homeier, H. Zhao, A. Bohrdt, F. Grusdt, P. Hauke, and J. Knolle, Enhancing Disorder-Free Localization through Dynamically Emer- gent Local Symmetries, PRX Quantum3, 020345 (2022)

    2022

  79. [79]

    Chakraborty, M

    N. Chakraborty, M. Heyl, P. Karpov, and R. Moess- ner, Disorder-free localization transition in a two- dimensional lattice gauge theory, Phys. Rev. B106, L060308 (2022)

    2022

  80. [80]

    C. Gao, Z. Tang, F. Zhu, Y. Zhang, H. Pu, and L. Chen, Nonthermal dynamics in a spin- 1 2 lattice Schwinger model, Phys. Rev. B107, 104302 (2023)

    2023

Showing first 80 references.