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Probing quantum many-body dynamics using subsystem Loschmidt echos

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Pith's one-line read The paper claims that the subsystem Loschmidt echo, a locally measurable string-overlap probability, captures dynamical quantum phase transitions and, through its late-time average, quantitatively reveals the dimension of the accessible…

desk verdict Solid experimental demonstration of the SLE as a probe of DQPTs and Hilbert-space fragmentation; the long-time dimension extraction needs an equilibration check for the ergodic domain-wall state. read the letter →

arxiv 2501.16995 v1 pith:H26AGI4P submitted 2025-01-28 cond-mat.quant-gas cond-mat.stat-mechphysics.atom-phquant-ph

Simon Karch , Souvik Bandyopadhyay , Zheng-Hang Sun , Alexander Impertro , SeungJung Huh , Irene Prieto Rodríguez , Julian F. Wienand , Wolfgang Ketterle
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Markus Heyl Anatoli Polkovnikov Immanuel Bloch Monika Aidelsburger
This is my paper · ORCID
classification cond-mat.quant-gascond-mat.stat-mechphysics.atom-phquant-ph
keywords subsystemLoschmidtechodynamicalquantumphasetransitionHilbertspacefragmentationaccessibledimensiongasmicroscopeBose-Hubbardmodelhigher-ordercorrelationsergodicitybreaking
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that a locally measurable quantity, the subsystem Loschmidt echo (the probability that a block of N adjacent sites still shows its initial occupation string at time t), carries the same deep information as the full return probability while remaining practical to measure. If true, a single snapshot-based observable would serve both sides of many-body physics: its short-time rate function locates a dynamical quantum phase transition, and its long-time average gives the effective thermodynamic entropy and hence the dimension of the Hilbert space a system can actually reach. The authors support this with ultracold-atom experiments in a one-dimensional Bose-Hubbard chain, showing a sharpening DQPT feature at about $t\approx 0.9\,\hbar/J$ and a linear growth of $-\ln L_N$ with $N$ that yields $(\dim\mathcal{H}_{\mathrm{eff}})^{1/L}\approx 2.3$ per site in the ergodic regime and about 1.5 versus 1.1 for two states in the fragmented regime. This matters because the full Loschmidt echo decays exponentially in system size, while the subsystem echo is robust and already informative for small blocks.

What carries the argument

The central object is the subsystem Loschmidt echo, defined as the spatial average of local projectors onto the initial occupation string, $L_N(t)=\frac{1}{L-N+1}\sum_{i=1}^{L-N+1}\langle\prod_{j=i}^{i+N-1}\hat P_j\rangle_t$. The short-time mechanism is the expansion of $L_N$ into connected density correlation functions, with each $n$-point term carrying irreducible information; the sharpening of the rate function as $N$ grows comes from higher-order terms acting at the critical time. The long-time mechanism is the identity $-\ln L_N = S_N(\beta,\mu) - \tfrac{1}{2}\beta^2\delta E^2 \le S_N(\beta,\mu)$, which converts a string probability into a thermodynamic entropy, plus the thermodynamic-limit relation $(\dim\mathcal{H}_{\mathrm{eff}})^{1/L}=\exp\!\left(\frac{d(-\ln L_N)}{dN}\right)$, which turns the measured slope into a Hilbert-space dimension per site.

What would settle it

Re-measure $-\ln L_N$ in later time windows, for example at 400, 600, and 1000 $\hbar/J$, for the same initial states; if the extracted slope changes or drifts monotonically, the quasi-equilibrium premise fails. Alternatively, fix $\beta$ from the measured density distribution and check the long-time identity with an independent estimate of the energy variance $\delta E^2$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the subsystem Loschmidt echo is defined as $L_N(t)=\frac{1}{L-N+1}\sum_{i=1}^{L-N+1}\langle\prod_{j=i}^{i+N-1}\hat P_j\rangle_t$, the spatial average of local projectors onto the initial occupation string. The central discovery is that this observable has two complementary readings. After a quench from a charge-density-wave state in the hard-core Bose-Hubbard regime ($U/J\approx 25$, $\Delta=0$), the rate function $-\ln L_N/N$ develops a progressively sharper kink near $t_c\approx 0.9\,\hbar/J$; expanding $L_N$ in connected density correlations shows that genuine three- and four-point correlations are what shape the kink. In the long-time regime ($t\approx 230\!-\!280\,\hbar/J$), the time-averaged value obeys $-\ln L_N = S_N(\beta,\mu) - \tfrac{1}{2}\beta^2\delta E^2 \le S_N(\beta,\mu)$, so its slope with $N$ becomes $(\dim\mathcal{H}_{\mathrm{eff}})^{1/L}=\exp\!\left(\frac{d(-\ln L_N)}{dN}\right)$. Measured values are $2.29(1)$ and $2.34(1)$ for domain-wall and CDW initial states in the ergodic regime, versus $1.54(1)$ and $1.12(1)$ in the fragmented regime, with the difference directly attributed to different Hilbert-space fragments.

Load-bearing premise

The load-bearing premise is that by about 230 to 280 $\hbar/J$ the system has reached quasi-equilibrium inside its accessible fragment, so the measured $-\ln L_N$ equals the equilibrium thermodynamic entropy; if it has not, the slope measures transient relaxation instead.

Editorial extensions

If this is right

  • If the central claim is right, any quantum simulator with site-resolved readout can measure dynamical quantum phase transitions through the subsystem Loschmidt echo without facing the exponentially small signal of the full Loschmidt echo.
  • In the same run, the slope of $-\ln L_N$ versus $N$ gives a quantitative, model-free estimate of the accessible Hilbert-space dimension per site in the thermodynamic limit.
  • The differing slopes for domain-wall and CDW states in the fragmented regime are direct evidence that those states live in different uncoupled fragments, i.e. ergodicity breaking by kinetic constraints.
  • The robustness of the subsystem Loschmidt echo against particle loss makes entropy and Hilbert-space-dimension measurements feasible in systems where the full return probability would vanish from any lost atom.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the extraction needs only site-resolved snapshots, the same protocol could be used to produce space- and time-resolved entropy maps, for example to watch a thermalization front move through a system or to detect localized regions in a many-body localized phase.
  • Editorial inference: the correction term in the long-time identity is a built-in thermometer; with an independent estimate of the energy variance, the difference between $-\ln L_N$ and the fitted thermodynamic entropy would calibrate an effective temperature for states that do not reach the infinite-temperature limit.
  • Editorial inference: the fact that high-order connected correlations dominate the kink suggests that string observables of length comparable to the correlation length could serve as sensitive detectors of rare many-body correlations in quenches beyond the charge-density-wave case studied here.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper experimentally introduces the subsystem Loschmidt echo (SLE) as a quasi-local observable that can be measured with a quantum gas microscope and demonstrates its utility in two regimes of the one-dimensional Bose-Hubbard model. In the short-time regime, after a quench from a charge-density-wave state in the hard-core limit, the SLE shows a sharpening kink-like feature around t ≈ 0.9 ħ/J that becomes more pronounced with increasing subsystem size N; the rate function −ln L_N/N develops a collapse for larger N, and the authors decompose L_N into connected density correlation functions, showing that genuine 3- and 4-point correlations dominate near the dynamical critical point. In the long-time regime, the time-averaged SLE is measured for subsystem sizes N = 1–5 in both an ergodic regime (U/J ≈ 2.7, Δ = 0) and a fragmented regime (U ≈ Δ, Δ/J ≈ 16.7). From the slope of −ln L_N versus N, the authors extract (dim H_eff)^{1/L} = 2.29(1) and 2.34(1) for the ergodic domain-wall and CDW states, and 1.54(1) and 1.12(1) for the fragmented domain-wall and CDW states, interpreting the reduction as direct evidence of Hilbert-space fragmentation. The results are compared with Krylov subspace, TEBD, and TDVP simulations, and the fragmented-regime slopes are also compared with a simple combinatorial counting based on the first-order effective Hamiltonian.

Significance. The SLE is a valuable new observable: it is exponentially less sensitive to noise than the full Loschmidt echo, it can be measured with existing quantum gas microscope techniques, and it gives access to both dynamical critical behavior and, through its long-time average, the effective Hilbert-space dimension. The short-time DQPT observation is convincing and is strengthened by the explicit decomposition into higher-order connected correlations and by the agreement with TEBD numerics. The long-time dimension extraction is supported by independent Krylov and TDVP simulations of the same Hamiltonian, which is a notable strength. If the equilibration premise is validated, the method provides a broadly applicable probe of ergodicity breaking and thermalization in quantum simulators. The paper is therefore of high significance for the quantum simulation and many-body physics communities.

major comments (3)
  1. [Long-time dynamics, Eq. (5), Table S2, Fig. S4] The central quantitative claim that the slope of −ln L_N versus N equals the thermodynamic entropy density and yields (dim H_eff)^{1/L} via Eq. (5) requires that the SLE has reached its quasi-equilibrium value by the measurement window t ≈ 230–280 ħ/J. This premise is not established for the ergodic domain-wall state: Table S2 shows that the extracted (dim H_eff)^{1/L} varies from 2.29(1) to 2.19(1) as the ROI increases from 20 to 40 sites, with a residual imbalance of 6–15%, and the numerical relaxation check in Fig. S4 is shown for the CDW ergodic and DW fragmented cases, not for the DW ergodic case. If the DW ergodic subsystem strings are still relaxing at the measurement time, the slope measures a transient rate rather than an entropy, and the agreement with Krylov numerics could be coincidental if the numerics are averaged over a similar non-equilibrated time window. Please provide a direct relaxation check (numerical or experimental) for the DW ergodic case and quantify the systematic error due to the ROI dependence.
  2. [Eq. (4)] The correction term ½ β² δE² in Eq. (4) is never quantified. The authors argue that β is small for high-energy initial states, but the domain-wall initial state in the ergodic regime may have a finite energy density, and the observed residual imbalance suggests non-equilibrated dynamics on the probed timescale. Please estimate β and δE² from the quench parameters or from the independent numerical simulations and show that ½ β² δE² is below the reported statistical error of the slopes; otherwise the reported values of (dim H_eff)^{1/L} may contain a finite-temperature offset that is not included in the error budget.
  3. [Fig. 3b and SI Sec. V.A] The linear fits used to extract the slopes in Fig. 3b are not documented in sufficient detail. In particular, the SI fits the numerical data in Fig. S13 with a line forced through the origin, but if the intercept is nonzero for the small subsystem sizes N = 1–5 probed experimentally, forcing through the origin biases the slope. Please report free linear fits with intercepts, their uncertainties, and the reduced chi-square for both the experimental and numerical data, and show the sensitivity of (dim H_eff)^{1/L} to excluding the N = 1 point.
minor comments (5)
  1. [Title and abstract] The word 'echos' in the title should be 'echoes'.
  2. [Main text, definition of SLE] The formal definition of the SLE in the paragraph after Eq. (1) contains garbled notation: 'L(i)N = DQi+N −1 i ˆPi E' should be rewritten as an expectation value of a product of local projectors, for example ⟨∏_{j=i}^{i+N-1} P̂_j⟩.
  3. [Main text, Fig. 2c] The exponential fit to τ_c^N is shown in Fig. 2c, but the fit function and the extracted parameters are not given in the main text; please provide them or refer explicitly to the SI equation (S19) and the fit results in Fig. S8.
  4. [Main text, page 5] The notation S_eff^N for the effective entropy is introduced but not defined; please define it explicitly and connect it to −ln L_N.
  5. [SI Sec. III.A.2] The post-selection on chain filling between 0.42 and 0.55 is described, but the effect of this post-selection on the SLE and its potential bias is not discussed; a sentence justifying the chosen window and its impact on the results would be helpful.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the SLE entropy–dimension relation is a standard identification, benchmarked against independent numerics and combinatorics.

full rationale

The paper's derivation chain is not circular. The central long-time relation rests on the identification of the measured long-time SLE with thermodynamic entropy. Although the paper writes −ln L_N ≡ S_eff^N, this is a notation; the physical content is the approximate equality −ln L_N ≈ S_N(β, μ) derived in the Supplementary Information from a boundary-partition-function/grand-canonical argument (Eqs. S12–S16), not assumed by definition. Equation (5), (dim H_eff)^{1/L} = exp(d(−ln L_N)/dN), is the standard Boltzmann relation S = ln(dim H_eff) applied to that entropy; the nontrivial experimental claim is that the measured slope equals the thermodynamic entropy density, which is separately checked against Krylov-subspace and TDVP simulations of the same Hamiltonian and against independent combinatorial fragment dimensions (√2 and 1). There is no fitted parameter renamed as a prediction: the experimental slopes are raw measured values, and the numerical benchmarks are not fitted to those slopes. The short-time DQPT claim relies on the prior theoretical framework of Refs. [30,31], which include coauthors of the present work, but those are published theoretical predictions that the experiment tests; they are not invoked as a uniqueness theorem, and the higher-order-correlation decomposition in Eq. (3) is an algebraic identity verified by TEBD numerics. The main limitations are correctness risks rather than circularity: the quasi-equilibration premise at t≈230–280 ħ/J is stated explicitly as an assumption, Table S2 reports a residual imbalance of ≈6–15% for the ergodic domain-wall state, and the β²δE² correction in Eq. (4) is not quantified experimentally. These affect the reliability of the interpretation, but they do not make the derivation equivalent to its inputs. The self-citations present are therefore not load-bearing, and the central derivations have independent content.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central derivation has a low axiom count for an experimental paper: the Bose-Hubbard model is standard, the main physical assumptions are thermalization within the accessible fragment and smallness of the beta^2 deltaE^2 correction, and the perturbative fragmentation Hamiltonian is standard. The free parameters are all data-analysis or calibration parameters; none of them is fitted to produce the central numerical predictions.

free parameters (3)
  • DQPT empirical fit parameters (alpha_N, beta_N, t_c^N, tau_c^N, c) = Not reported as single values; fits shown in Fig. S8
    Used in Eq. S19 to extract the sharpening timescale tau_c^N; the exponential scaling in Fig. 2c rests on this empirical fit.
  • Exponential scaling fit for tau_c^N (amplitude, decay rate) = Not quoted in text
    Main text Fig. 2c; fitted to N=1-5, with N=6,7 excluded because the reduced chi-square exceeds 3.
  • Imperfection-model rates (atom loss p=10%, initial-state errors 5%/1%) = 0.10, 0.05, 0.01
    SI Section V B; chosen so that numerics reproduce the measured fragmented-regime dimensions; these rates are not independently measured.
assumptions (5)
  • domain assumption The dynamics is governed by the single-band Bose-Hubbard model Eq. (2) with calibrated J, U, and Delta.
    Standard model for the optical lattice; assumes no higher bands, no significant losses, and negligible triple occupancies (checked numerically).
  • domain assumption In the long-time regime the diagonal ensemble is equivalent to the grand-canonical ensemble for thermalizing states (ETH).
    Used in SI II C to identify -ln L_N with thermodynamic entropy; not proven for the specific finite-time dynamics.
  • ad hoc to paper For high-energy initial states beta is small enough that the 1/2 beta^2 deltaE^2 correction in Eq. (4) is negligible.
    No quantitative estimate of beta or deltaE^2 is provided; the extraction of S_N from the SLE assumes this correction is small.
  • ad hoc to paper For Delta much larger than J with Delta about U, the first-order effective Hamiltonian Eq. (6) captures the dynamics on the experimental time window, with higher-order couplings negligible.
    Used to predict fragment dimensions sqrt(2) and 1; the paper states that higher-order couplings eventually lead to full thermalization at longer times.
  • standard math Jensen's inequality and the cumulant expansion apply to the boundary partition function.
    Used in SI Eqs. S14-S16 to bound and approximate -ln L_N.

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Pith. "Pith review of Probing quantum many-body dynamics using subsystem Loschmidt echos." pith.science (2026). https://pith.science/paper/H26AGI4P

@misc{pith2026250116995,
  author       = {Pith},
  title        = {Pith review of: Probing quantum many-body dynamics using subsystem Loschmidt echos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H26AGI4P}},
  note         = {Machine review of arXiv:2501.16995}
}
read the original abstract

The Loschmidt echo - the probability of a quantum many-body system to return to its initial state following a dynamical evolution - generally contains key information about a quantum system, relevant across various scientific fields including quantum chaos, quantum many-body physics, or high-energy physics. However, it is typically exponentially small in system size, posing an outstanding challenge for experiments. Here, we experimentally investigate the subsystem Loschmidt echo, a quasi-local observable that captures key features of the Loschmidt echo while being readily accessible experimentally. Utilizing quantum gas microscopy, we study its short- and long-time dynamics. In the short-time regime, we observe a dynamical quantum phase transition arising from genuine higher-order correlations. In the long-time regime, the subsystem Loschmidt echo allows us to quantitatively determine the effective dimension and structure of the accessible Hilbert space in the thermodynamic limit. Performing these measurements in the ergodic regime and in the presence of emergent kinetic constraints, we provide direct experimental evidence for ergodicity breaking due to fragmentation of the Hilbert space. Our results establish the subsystem Loschmidt echo as a novel and powerful tool that allows paradigmatic studies of both non-equilibrium dynamics and equilibrium thermodynamics of quantum many-body systems, applicable to a broad range of quantum simulation and computing platforms.

Figures

Figures reproduced from arXiv: 2501.16995 by the authors.

Figure 1
Figure 1. Subsystem Loschmidt echo (SLE) and schematic of the experiment. a, Schematic of the quan￾tum gas microscope (QGM) resolving dynamics in the 1D Bose-Hubbard model with tunnel coupling J, on-site inter￾action U, and staggered potential ∆. b, Illustration of den￾sity snapshots for the initial state |ψ0⟩ = |. . . 101010 . . .⟩ and time-evolved state |ψ(t)⟩. The SLE measures the probability of finding the initial state b… view at source ↗
Figure 2
Figure 2. Short-time dynamics: dynamical quantum phase transition. a, SLE evaluated for subsystem sizes N = 1−7 in the central 32 sites of 40-site long chains to avoid edge effects. A DQPT emerges at tc ≈ 0.9ℏ/J [J/h =155(2) Hz, ℏ/ = h/(2π) is the reduced Planck’s constant]. Error bars are estimated using standard error of proportion and, when not visible, are smaller than the marker. Every data point around the peak was obta… view at source ↗
Figure 3
Figure 3. Long-time dynamics: structure and dimension of the many-body Hilbert space. a, The staggered 1D BHM in ergodic and fragmented regimes. In the ergodic regime, both the CDW and domain wall initial states explore the entire Hilbert space. For strong kinetic constraints, the two initial states live in different fragments of the Hilbert space. b, Time-averaged −ln LN as a function of the subsystem size N. We take the spa… view at source ↗

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Reference graph

Works this paper leans on

82 extracted references · 61 canonical work pages · cited by 10 Pith papers

  1. [1]

    Gross and W

    C. Gross and W. S. Bakr, Nature Physics17, 1316 (2021)

    2021

  2. [2]

    Browaeys and T

    A. Browaeys and T. Lahaye, Nature Physics 16, 132 (2020)

    2020

  3. [3]

    Kjaergaard, M

    M. Kjaergaard, M. E. Schwartz, J. Braum¨ uller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Annual Review of Condensed Matter Physics 11, 369 (2020)

    2020

  4. [4]

    Foss-Feig, G

    M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Annual Review of Condensed Matter Physics (2024)

    work page 2024

  5. [5]

    The Loschmidt echo coincides with the return probability when |ψ0⟩ is an eigenstate of ˆH1, and thus the return probability and the Loschmidt echo are often used as synonyms

    The Loschmidt echo is often defined in the con- text of time-reversal experiments as L(t) = |⟨ψ0|ei ˆH2t/ℏe−i ˆH1t/ℏ|ψ0⟩|2, where the forward time- evolution is governed by Hamiltonian ˆH1 and the time-reversal process is governed by ˆH2 [67]. The Loschmidt echo coincides with the return probability when |ψ0⟩ is an eigenstate of ˆH1, and thus the return p...

    work page

  6. [6]

    P. V. Coveney, Nature 333, 409 (1988)

    work page 1988

  7. [7]

    Peres, Physical Review A 30, 1610 (1984)

    A. Peres, Physical Review A 30, 1610 (1984)

    work page 1984

  8. [8]

    Gorin, T

    T. Gorin, T. Prosen, T. H. Seligman, and M. ˇZnidariˇ c, Physics Reports 435, 33 (2006)

    work page 2006

Show all 82 references
  1. [9]

    Haake, S

    F. Haake, S. Gnutzmann, and M. Ku´ s, Quantum Signa- tures of Chaos, Springer Series in Synergetics (Springer International Publishing, Cham, 2018)

    2018

  2. [10]

    E. J. Torres-Herrera and L. F. Santos, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, 20160434 (2017)

    2017

  3. [11]

    Schwinger, Physical Review 82, 664 (1951)

    J. Schwinger, Physical Review 82, 664 (1951)

    1951

  4. [12]

    T. D. Cohen and D. A. McGady, Physical Review D 78, 036008 (2008)

    2008

  5. [13]

    Touchette, Physics Reports 478, 1 (2009)

    H. Touchette, Physics Reports 478, 1 (2009)

    2009

  6. [14]

    E. J. Torres-Herrera and L. F. Santos, Physical Review B 92, 014208 (2015)

    2015

  7. [15]

    Serbyn and D

    M. Serbyn and D. A. Abanin, Physical Review B 96, 014202 (2017)

    2017

  8. [16]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, Nature Physics14, 745 (2018)

    2018

  9. [17]

    Serbyn, D

    M. Serbyn, D. A. Abanin, and Z. Papi´ c, Nature Physics 17, 675 (2021)

    2021

  10. [18]

    Z. Li, S. Colombo, C. Shu, G. Velez, S. Pilatowsky- Cameo, R. Schmied, S. Choi, M. Lukin, E. Pedrozo- Pe˜ nafiel, and V. Vuleti´ c, Science380, 1381 (2023)

    2023

  11. [19]

    Colombo, E

    S. Colombo, E. Pedrozo-Pe˜ nafiel, A. F. Adiyatullin, Z. Li, E. Mendez, C. Shu, and V. Vuleti´ c, Nature Physics 18, 925 (2022)

    2022

  12. [20]

    Davis, G

    E. Davis, G. Bentsen, and M. Schleier-Smith, Physical Review Letters 116, 053601 (2016)

    2016

  13. [21]

    Pedrozo-Pe˜ nafiel, S

    E. Pedrozo-Pe˜ nafiel, S. Colombo, C. Shu, A. F. Adiy- atullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, and V. Vuleti´ c, Nature588, 414 (2020)

    2020

  14. [22]

    Macr ` ı, A

    T. Macr ` ı, A. Smerzi, and L. Pezz` e, Physical Review A 94, 010102 (2016)

    2016

  15. [23]

    Jurcevic, H

    P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Physical Review Letters 119, 080501 (2017)

    2017

  16. [24]

    E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt, Nature 534, 516 (2016)

    2016

  17. [25]

    Z.-H. Zhu, Y. Liu, G. Lagnese, F. M. Surace, W.-Y. Zhang, M.-G. He, J. C. Halimeh, M. Dalmonte, S. C. Morampudi, F. Wilczek, Z.-S. Yuan, and J.-W. Pan, arXiv:2411.12565 (2024)

    2024 arXiv

  18. [26]

    Braum¨ uller, A

    J. Braum¨ uller, A. H. Karamlou, Y. Yanay, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, B. M. Niedzielski, Y. Sung, A. Veps¨ al¨ ainen, R. Winik, J. L. Yoder, T. P. Orlando, S. Gustavsson, C. Tahan, and W. D. Oliver, Nature Physics 18, 172 (2022)

    2022

  19. [27]

    A. Cao, R. Sajjad, H. Mas, E. Q. Simmons, J. L. Tan- limco, E. Nolasco-Martinez, T. Shimasaki, H. E. Kon- dakci, V. Galitski, and D. M. Weld, Nature Physics 18, 1302 (2022)

    2022

  20. [28]

    Singh, C

    K. Singh, C. J. Fujiwara, Z. A. Geiger, E. Q. Sim- mons, M. Lipatov, A. Cao, P. Dotti, S. V. Rajagopal, R. Senaratne, T. Shimasaki, M. Heyl, A. Eckardt, and D. M. Weld, Physical Review X 9, 041021 (2019)

    2019

  21. [30]

    Bandyopadhyay, A

    S. Bandyopadhyay, A. Polkovnikov, and A. Dutta, Phys- ical Review Letters 126, 200602 (2021)

    2021

  22. [31]

    J. C. Halimeh, D. Trapin, M. Van Damme, and M. Heyl, Physical Review B 104, 075130 (2021)

    2021

  23. [32]

    Zhang, H

    P. Zhang, H. Dong, Y. Gao, L. Zhao, J. Hao, J.-Y. De- saules, Q. Guo, J. Chen, J. Deng, B. Liu, W. Ren, Y. Yao, X. Zhang, S. Xu, K. Wang, F. Jin, X. Zhu, B. Zhang, H. Li, C. Song, Z. Wang, F. Liu, Z. Papi´ c, L. Ying, H. Wang, and Y.-C. Lai, Nature Physics 19, 120 (2023)

    2023

  24. [33]

    Impertro, J

    A. Impertro, J. F. Wienand, S. H¨ afele, H. Von Raven, S. Hubele, T. Klostermann, C. R. Cabrera, I. Bloch, and M. Aidelsburger, Communications Physics 6, 166 (2023)

    2023

  25. [35]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Reports on Progress in Physics 85, 086501 (2022)

    2022

  26. [36]

    M. Heyl, A. Polkovnikov, and S. Kehrein, Physical Re- 1 view Letters 110, 135704 (2013)

    2013

  27. [37]

    Heyl, Reports on Progress in Physics 81, 054001 (2018)

    M. Heyl, Reports on Progress in Physics 81, 054001 (2018)

    2018

  28. [38]

    Baek and Y

    Y. Baek and Y. Kafri, Journal of Statistical Mechanics: Theory and Experiment 2015, P08026 (2015)

    2015

  29. [39]

    Meibohm and M

    J. Meibohm and M. Esposito, Physical Review Letters 128, 110603 (2022)

    2022

  30. [40]

    Fl¨ aschner, D

    N. Fl¨ aschner, D. Vogel, M. Tarnowski, B. S. Rem, D.-S. L¨ uhmann, M. Heyl, J. C. Budich, L. Mathey, K. Seng- stock, and C. Weitenberg, Nature Physics14, 265 (2018)

    2018

  31. [41]

    Zhang, G

    J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Nature 551, 601 (2017)

    2017

  32. [42]

    Xu, Z.-H

    K. Xu, Z.-H. Sun, W. Liu, Y.-R. Zhang, H. Li, H. Dong, W. Ren, P. Zhang, F. Nori, D. Zheng, H. Fan, and H. Wang, Science Advances 6, eaba4935 (2020)

    2020

  33. [43]

    Zheng, W.-Y

    Y.-G. Zheng, W.-Y. Zhang, Y.-C. Shen, A. Luo, Y. Liu, M.-G. He, H.-R. Zhang, W. Lin, H.-Y. Wang, Z.-H. Zhu, M.-C. Chen, C.-Y. Lu, S. Thanasilp, D. G. Angelakis, Z.-S. Yuan, and J.-W. Pan, arXiv:2210.08556 (2022)

    2022 arXiv

  34. [44]

    Schweigler, V

    T. Schweigler, V. Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges, and J. Schmiedmayer, Nature 545, 323 (2017)

    2017

  35. [45]

    S. S. Hodgman, R. G. Dall, A. G. Manning, K. G. H. Baldwin, and A. G. Truscott, Science 331, 1046 (2011)

    2011

  36. [46]

    R. G. Dall, A. G. Manning, S. S. Hodgman, W. RuGway, K. V. Kheruntsyan, and A. G. Truscott, Nature Physics 9, 341 (2013)

    2013

  37. [48]

    Koepsell, D

    J. Koepsell, D. Bourgund, P. Sompet, S. Hirthe, A. Bohrdt, Y. Wang, F. Grusdt, E. Demler, G. Salomon, C. Gross, and I. Bloch, Science 374, 82 (2021)

    2021

  38. [49]

    Kardar, Statistical Physics of Fields, 1st ed

    M. Kardar, Statistical Physics of Fields, 1st ed. (Cam- bridge University Press, 2007)

    2007

  39. [50]

    Paredes, A

    B. Paredes, A. Widera, V. Murg, O. Mandel, S. F¨ olling, I. Cirac, G. V. Shlyapnikov, T. W. H¨ ansch, and I. Bloch, Nature 429, 277 (2004)

    2004

  40. [51]

    Cheneau, P

    M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauß, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, and S. Kuhr, Nature 481, 484 (2012)

    2012

  41. [53]

    Avdoshkin and A

    A. Avdoshkin and A. Dymarsky, Physical Review Re- search 2, 043234 (2020)

    2020

  42. [54]

    A. H. Karamlou, J. Braum¨ uller, Y. Yanay, A. Di Paolo, P. M. Harrington, B. Kannan, D. Kim, M. Kjaer- gaard, A. Melville, S. Muschinske, B. M. Niedzielski, A. Veps¨ al¨ ainen, R. Winik, J. L. Yoder, M. Schwartz, C. Tahan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, npj Qu...

    2022

  43. [56]

    Khemani, M

    V. Khemani, M. Hermele, and R. Nandkishore, Physical Review B 101, 174204 (2020)

    2020

  44. [57]

    S. Pai, M. Pretko, and R. M. Nandkishore, Physical Re- view X 9, 021003 (2019)

    2019

  45. [58]

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Poll- mann, Physical Review X 10, 011047 (2020)

    2020

  46. [59]

    Kohlert, S

    T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Physical Review Letters 130, 010201 (2023)

    2023

  47. [61]

    Adler, D

    D. Adler, D. Wei, M. Will, K. Srakaew, S. Agrawal, P. Weckesser, R. Moessner, F. Pollmann, I. Bloch, and J. Zeiher, Nature 636, 80 (2024)

    2024

  48. [62]

    Alhassid and R

    Y. Alhassid and R. D. Levine, Phys. Rev. A 46, 4650 (1992)

    1992

  49. [63]

    H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, arXiv:2403.12021 (2024)

    2024 arXiv

  50. [64]

    K. Kwon, K. Kim, J. Hur, S. Huh, and J.-y. Choi, Phys- ical Review A 105, 033323 (2022)

    2022

  51. [65]

    R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zei- her, Physical Review Letters 133, 013401 (2024)

    2024

  52. [66]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Re- views of Modern Physics 91, 021001 (2019)

    2019

  53. [67]

    Goussev, R

    A. Goussev, R. A. Jalabert, H. M. Pastawski, and D. A. Wisniacki, Scholarpedia 7, 11687 (2012). Supplementary Information for: Probing quantum many-body dynamics using subsystem Loschmidt echos CONTENTS I. Experimental details 2 A. Experimental sequence 2 B. Doublon splitting ...

    2012

  54. [68]

    Short-time dynamics 9

  55. [69]

    Subsystem Loschmidt echo evaluation 10 C

    Long-time dynamics 9 B. Subsystem Loschmidt echo evaluation 10 C. Extraction of the DQPT sharpness 11 D. DQPT numerics with imperfect initial state 11 IV. Effective Hilbert space dimension and fragmentation 11 V. Long-time regime numerics 13 A. Numerical results for perfect in...

  56. [70]

    During post-selection, we filter out approximately 20% of the chains with filling lower than 0.42 and higher than 0 .55

    Short-time dynamics During short-time dynamics, we do not detect any atom loss in the ROI of size 32 × 32 within a box po- tential of 40 × 40 lattice sites. During post-selection, we filter out approximately 20% of the chains with filling lower than 0.42 and higher than 0 .55....

  57. [71]

    We again post-select on chains that have a filling less than 0 .42 and above 0 .55

    Long-time dynamics As we have described above, for the long-time dynam- ics, we prepare the initial state only in every other chain, leaving the remaining half of the chains empty for subse- quent doublon detection to avoid parity projection during the fluorescence imaging. We...

    2000

  58. [72]

    the CDW initial state |010101010101⟩,

  59. [73]

    the single-domain-wall (sDW) initial state |111111000000⟩ and

  60. [74]

    Under the effective Hamiltonian defined in Eq

    the double-domain-wall (dDW) initial state |000111111000⟩. Under the effective Hamiltonian defined in Eq. (S24), the CDW initial state is a completely frozen state, and the dimension of the corresponding fragment is equal to

  61. [75]

    The results of this calculation are shown in Fig

    For the single- and double-domain-wall initial states, we can directly calculate the dimensions of the fragments by counting the number of allowed configurations. The results of this calculation are shown in Fig. S10a. We note that the double-domain-wall state corresponds to t...

  62. [76]

    Impertro, J

    A. Impertro, J. F. Wienand, S. H¨ afele, H. Von Raven, S. Hubele, T. Klostermann, C. R. Cabrera, I. Bloch, and M. Aidelsburger, Communications Physics 6, 166 (2023). b a c Figure S15. Effect of imperfections on the SLE. a, Numerical results (Krylov subspace method) for the tim...

    2023

  63. [77]

    J. F. Wienand, S. Karch, A. Impertro, C. Schweizer, E. McCulloch, R. Vasseur, S. Gopalakrishnan, M. Aidels- burger, and I. Bloch, Nature Physics 20, 1732 (2024)

    2024

  64. [78]

    Impertro, S

    A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Physical Review Letters 133, 063401 (2024)

    2024

  65. [79]

    Impertro, S

    A. Impertro, S. Huh, S. Karch, J. F. Wienand, I. Bloch, and M. Aidelsburger, arXiv:2412.09481 (2024)

    2024

  66. [80]

    Scherg, T

    S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Nature Communications 12, 4490 (2021)

    2021

  67. [81]

    J. P. Ronzheimer, M. Schreiber, S. Braun, S. S. Hodg- man, S. Langer, I. P. McCulloch, F. Heidrich-Meisner, I. Bloch, and U. Schneider, Physical Review Letters 110, 205301 (2013)

    2013

  68. [82]

    Rispoli, A

    M. Rispoli, A. Lukin, R. Schittko, S. Kim, M. E. Tai, J. L´ eonard, and M. Greiner, Nature573, 385 (2019)

    2019

  69. [83]

    Hauschild, J

    J. Hauschild, J. Unfried, S. Anand, B. Andrews, M. Bintz, U. Borla, S. Divic, M. Drescher, J. Geiger, M. Hefel, K. H´ emery, W. Kadow, J. Kemp, N. Kirchner, V. S. Liu, G. M¨ oller, D. Parker, M. Rader, A. Romen, S. Scalet, L. Schoonderwoerd, M. Schulz, T. Soejima, P. Thoma, Y....

    2024

  70. [84]

    Rigol, V

    M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008)

    2008

  71. [85]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, Advances in Physics 65, 239 (2016)

    2016

  72. [86]

    M. Heyl, A. Polkovnikov, and S. Kehrein, Physical Re- view Letters 110, 135704 (2013)

    2013

  73. [87]

    Q. Guo, C. Cheng, Z.-H. Sun, Z. Song, H. Li, Z. Wang, W. Ren, H. Dong, D. Zheng, Y.-R. Zhang, R. Mondaini, H. Fan, and H. Wang, Nature Physics 17, 234 (2021)

    2021

  74. [88]

    Fishman, S

    M. Fishman, S. White, and E. Stoudenmire, SciPost Physics Codebases , 4 (2022)

    2022

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