Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

Roughening dynamics of interfaces in the two-dimensional quantum Ising model

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read The roughening transition controls how long flat quantum interfaces stay stable in the two-dimensional quantum Ising model, with smooth interfaces showing long-lived prethermal plateaus and rough ones decaying quickly.

desk verdict Solid numerics establish prethermal plateaus in the 2D TFIM, but the claim that the roughening transition controls relaxation is inferred from an effective model, not directly observed in the full model. read the letter →

arxiv 2412.10145 v2 pith:KN2DHEHT submitted 2024-12-13 quant-ph cond-mat.stat-mech

Wladislaw Krinitsin , Niklas Tausendpfund , Matteo Rizzi , Markus Heyl , Markus Schmitt This is my paper · ORCID
classification quant-phcond-mat.stat-mech MSC 82B2082B2682B80 PACS 05.30.-d75.10.Jm68.35.Ct
keywords quantumIsingmodelinterfacerougheningtransitiondomainwalldynamicsprethermalizationtreetensornetworkssolid-on-solidBKTRydbergsimulators
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

This paper tries to establish that the equilibrium roughening transition of interfaces has a sharp dynamical signature in the two-dimensional transverse-field Ising model. Starting from a straight domain wall, smooth interfaces below the critical transverse field exhibit long-lived prethermal plateaus, whereas above the roughening transition the domain wall decays quickly. The authors derive a one-dimensional solid-on-solid effective model for a single domain-wall profile per column and show that its dynamics match the full two-dimensional tensor-network simulation quantitatively up to $g/J \approx 1$. If correct, this identifies a distinct, non-perturbative mechanism for prethermalization, separate from proximity to integrability, Hilbert-space fragmentation, or quantum scars, and one that is directly testable in Rydberg atom arrays.

What carries the argument

The argument is carried by the effective Hamiltonian $H_{\mathrm{eff}} = 2J \sum_i |N_i - N_{i+1}| - g \sum_i (E_i + E_i^\dagger)$, where the height operators $N_i$ measure the perpendicular displacement of the interface in column $i$ and $E_i^\dagger, E_i$ flip spins next to the wall, obeying $[E_i, N_j] = E_i \delta_{i,j}$. This projection onto single-valued interface configurations, with no bubbles or overhangs, maps interface dynamics onto a one-dimensional quantum-rotor/solid-on-solid problem. The order parameter is the kink operator $K_\alpha(l) = \cos\big(\alpha(N_1 - N_l)\big)$, which equals 1 for a flat smooth interface and tends to 0 for a rough one; it is evaluated both in ground states, via uniform matrix-product-state methods, and in classical thermal states, via an exact transfer-matrix solution. The same operator, with bulk contributions divided out, provides the quantitative comparison between the full 2D tree-tensor-network dynamics and the effective model.

What would settle it

Simulate or measure the full two-dimensional dynamics at $g/J = 0.75$ to $1.0$ beyond $tJ = 100$, for example in a Rydberg atom array or with a larger tensor-network simulation, and record both the horizontal domain-wall length $D_x/L_x$ and the modified kink operator. If $D_x/L_x$ drops appreciably below 1, or if the kink plateau decays within a time that does not grow rapidly as the field approaches the inferred roughening transition, then the single-domain-wall projection and the roughening-controlled prethermalization claim are falsified.

Watch

Extended reading notes

Core claim

The central discovery is that the relaxation of a flat interface in the 2D quantum Ising model is governed by the same physics as the roughening transition. Projecting the dynamics onto states with exactly one horizontal interface segment per column yields an effective one-dimensional solid-on-solid model whose ground state has a smooth-to-rough Berezinskii-Kosterlitz-Thouless transition at $g_R/J \approx 1.38$; within the smooth regime the effective model thermalizes while the initially flat profile remains stable, which in the full model appears as prethermal plateaus in the imbalance and the modified kink operator. Large-scale tree tensor network simulations of the full 2D dynamics agree quantitatively with matrix-product-state simulations of the effective model for $g/J \leq 1$, including late-time plateau values on $8 \times 8$ and $16 \times 16$ lattices. In the classical limit of the effective model the smooth-interface phase is only a finite-size effect, with the crossover temperature vanishing as $1/\log L_x$, but the smooth regime survives to very large system sizes, which the authors argue is relevant for current experiments.

Load-bearing premise

The load-bearing premise is that the interface stays single-valued, with exactly one horizontal domain-wall segment per column and no bubbles or overhangs; this is validated only indirectly by $D_x/L_x$ remaining near 1 for $g/J \leq 1$ up to the simulated times, and if multi-segment configurations become important at longer times or larger fields, the effective model and the inferred link to the roughening transition would break down.

Editorial extensions

If this is right

  • For $g/J \lesssim 1$ the initially flat domain wall remains essentially frozen up to at least $tJ \approx 100$ on an $8 \times 8$ lattice and $tJ \approx 30$ on a $16 \times 16$ lattice; since level-spacing statistics are GOE-like, the eventual fate is thermalization, so the plateaus are prethermal rather than equilibrium order.
  • The mechanism does not rely on emergent conservation laws or Hilbert-space fragmentation, because the horizontal domain-wall length $D_x$ changes from its initial value during the dynamics; it therefore adds a distinct route to prethermalization.
  • The effective one-dimensional model is quantitatively predictive for the full two-dimensional interface dynamics in the tested regime, and the imbalance and kink operator are directly measurable through snapshots in Rydberg atom quantum simulators.
  • The inferred roughening transition at $g_R/J \approx 1.38$ marks the upper bound where the single-domain-wall description works; above it the interface is expected to decay quickly, although the full two-dimensional model is not directly simulated there.
  • The smooth-interface regime persists in finite systems up to very large sizes because the classical crossover temperature scales as $T_R \sim 1/\log L_x$, so current experimental system sizes should display the prethermal plateaus even though the thermodynamic classical limit roughens at any positive temperature.

Reading between the lines

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

  • Editorial inference: if the mechanism is robust, the smooth-interface regime of a two-dimensional Ising-type simulator acts as a tunable metastable memory whose lifetime is set by the distance to the roughening transition, suggesting that the roughening transition could be used to control decoherence in quantum simulation platforms.
  • Editorial inference: the same single-interface projection should apply to non-straight profiles such as zigzag walls, curved interfaces, and false-vacuum bubbles, so roughening may set the timescale for their straightening or decay; the paper lists these as future directions but does not make quantitative predictions for them.
  • Editorial inference: the paper validates the effective model only for $g/J \leq 1$ and up to the simulated times; a direct full two-dimensional simulation of the rough regime, $g/J > 1$, is not performed because separating bulk from interface contributions becomes infeasible, so the rapid decay above the transition remains an extrapolation from the effective model rather than a directly simulated
  • Editorial inference: the logarithmic dependence of $T_R$ on system size means that distinguishing a genuine roughening transition from a finite-size crossover in the full model will require careful scaling analysis; measuring the kink correlator as a function of system size and transverse field in a Rydberg array would be a direct test of the BKT character.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper studies the real-time dynamics of flat domain-wall interfaces in the two-dimensional transverse-field Ising model using large-scale tree tensor network simulations. For transverse fields up to g/J ≈ 1 the authors observe long-lived prethermal plateaus in the magnetization imbalance and in a modified kink operator. To explain these plateaus, they introduce an effective one-dimensional solid-on-solid model (Eq. 3) obtained by projecting onto single-domain-wall states with one horizontal interface segment per column. Using VUMPS in the thermodynamic limit, they locate a BKT roughening transition in the effective model at gR/J ≈ 1.38 and give an analytic treatment of the classical limit where the smooth-interface crossover temperature vanishes logarithmically with system size. The effective model is shown to quantitatively match the full-model dynamics for the kink operator up to g/J = 1. The central claim is that the roughening transition controls the relaxation of interfaces: smooth interfaces exhibit prethermal stability, while rough interfaces decay quickly, constituting a new prethermalization mechanism distinct from fragmentation or proximity to integrability.

Significance. If established, the connection between the interface roughening transition and the relaxation dynamics of domain walls would be a genuinely new mechanism for prethermalization in a two-dimensional quantum many-body system, with direct implications for Rydberg-atom quantum simulators. The paper has several clear strengths: the full-model TTN simulations are checked against multiple bond dimensions up to χ = 362; the comparison between the full model and the effective model is quantitative and favorable in the accessible regime; the classical-limit analysis is solved essentially exactly via a transfer-matrix diagonalization, leading to the closed-form prediction (5); and the authors release data and code. The main weakness is that the load-bearing connection between roughening and fast decay is inferred from the effective model rather than directly demonstrated in the full 2D model: full-model interface observables are only validated for g/J ≤ 1, while the claimed transition lies at gR/J ≈ 1.38. The paper is therefore an interesting and well-executed study whose headline conclusion currently outruns the direct numerical evidence.

major comments (3)
  1. [Dynamical signature of roughening (Fig. 3, SM Fig. S6b)] The central dichotomy — smooth interfaces show prethermal plateaus, rough interfaces decay quickly — is not directly established in the full 2D model. The modified kink operator KM is presented only for g/J ≤ 1 in Fig. 3b,c, and the SM explicitly states that separating bulk and interface contributions becomes infeasible for g/J > 1, with the unphysical growth in Fig. S6b flagged as an artifact of the method. The roughening transition is located in the effective model at gR/J ≈ 1.38 (End Matter), which lies outside the validated range of the full-model comparison. Consequently, the fast-decay regime is inferred from the effective-model phase diagram (Fig. 2d) rather than observed with an interface order parameter in the full model. This is load-bearing because 'above the roughening transition the domain wall decays quickly' is half of the paper's central claim. Please either provide a full-model observable that can be followed through gR (for example, a different bulk-subtraction scheme, or the late-time behavior of the bare kink operator with a quantitative error estimate) or explicitly present the roughening–relaxation link as a prediction of the effective model rather than a demonstrated property of the full 2D dynamics.
  2. [Effective model and its validation (Eq. 3, Fig. 3a, SM Fig. S7a)] The single-domain-wall projection excludes bubbles and overhangs, and its direct validation rests on the horizontal domain-wall length Dx/Lx staying close to one for g/J ≤ 1 up to the simulated times. Since the claimed transition lies at g/J ≈ 1.38, the subspace is not verified in precisely the regime where the transition occurs in the effective model. If bubble-pair or overhang degrees of freedom proliferate before gR in the full model, the effective model could either misplace the transition or miss its preemption. A quantitative estimate of the weight outside the single-domain-wall subspace as a function of g and t — for example, the fraction of columns with more than one horizontal interface segment, or the density of vertical domain-wall pairs — would substantiate the projection at and above the transition. As it stands, the projection is a controlled approximation only in the smooth regime, which is also the regime where the full-model comparison is available.
  3. [End Matter (BKT fit, Fig. 4b,c)] The location of the roughening transition relies on VUMPS data with Nmax ≤ 14, and the manuscript itself states that for Nmax = 14 the points around the transition are not yet fully converged and show numerical artifacts for g > gR. The BKT correlation-length fit to Eq. (6) is performed on this Nmax = 14 data up to g/J = 1.385, i.e., close to the fitted gR/J ≈ 1.38. It would materially strengthen the determination of gR to include an extrapolation in 1/Nmax or data at Nmax = 16 for a few points near gR, so that the fitted critical point is not controlled by unconverged data. This matters because Fig. 2d uses gR as the boundary separating smooth and rough interface regimes in the full model.
minor comments (6)
  1. [Introduction] The name 'Berezinski-Kosterlitz-Thouless' should be corrected to 'Berezinskii-Kosterlitz-Thouless' for consistency with the later usage 'Berezinskii–Kosterlitz–Thouless'.
  2. [Interface dynamics] In the sentence 'Next, we turn towards the question wether its signatures survive even at non-zero temperatures', 'wether' should be 'whether'.
  3. [Interface dynamics (footnote 1)] The phrase 'timescales which scale exponentially with J/g 1' is confusing because the footnote marker '1' follows the expression as if it were part of the formula; consider moving the footnote marker or rewriting the sentence.
  4. [Effective model] The SM derivation writes the vertical contribution as proportional to ∑|N_i − N_{i−1}|, while Eq. (3) in the main text uses |N_i − N_{i+1}|; aligning the index convention or explicitly stating the open-boundary convention would avoid confusion.
  5. [SM, Kink operator] In the sentence 'We want to stress that the observed rising of the kink operator an artifact of the method and not a physical effect', the verb 'is' is missing before 'an artifact'.
  6. [Discussion] The sentence 'More generally, the impact of curvature on the phenomenology of the roughening dynamics remains to be explored' is a suitable outlook, but the earlier statement that 'the results presented here rely on a Z2 symmetry-broken phase' would benefit from a brief explanation of how the Z2 structure enters the effective model, which is not explicitly Z2-symmetric.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: prethermal plateaus are direct TTN observations, the effective model is explicitly validated against full dynamics, and the main shortfall (no full-model interface data above g/J=1) is an evidence gap, not a circular construction.

full rationale

The central phenomenon is not manufactured. The imbalance plateaus of Fig. 1b are obtained directly from full TTN simulations before the effective model of Eq. (3) is introduced, and the effective model is an explicit projection of H onto the single-interface subspace, not a fit to the dynamics. Its validity is checked against the full model through Dx/Lx (Fig. 3a, Fig. S7a) and through direct comparison of the running-averaged kink operator (Fig. 3b,c), where the full-model value is evaluated on the unprojected 2D state. The roughening location gR/J ≈ 1.38 comes from a BKT correlation-length fit of the effective model in the End Matter, independent of the full dynamics, and the finite-temperature crossover formula (5) is derived analytically from the transfer-matrix solution and then verified numerically. The paper itself flags the important limitation: "We don't show data for transverse fields beyond g/J = 1, as bulk and interface contributions become increasingly difficult to disentangle" (Fig. 3b caption), so the fast-decay side of the dichotomy above gR is inferred from the imbalance and the effective-model phase diagram rather than directly observed with an interface order parameter; this is an evidence gap and a falsifiability concern, not a circular reduction. A mild caveat is that the kink angle is chosen in part for "best agreement between the effective and full model" (SM), so the quantitative match is not fully parameter-free, but the plateau existence and the Dx validation do not depend on that choice. No fit parameter is renamed as a prediction, and no load-bearing premise rests on a self-citation.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim (prethermal plateaus linked to a smooth-interface regime) rests on the numerical observation of plateaus (supported by TTN convergence), and on the effective model's phase diagram. The effective model introduces a projection to single-domain-wall states and a truncation Nmax; the roughening transition location gR is fitted. The QMC effective temperature and the level-spacing thermalization assumption are additional inputs. The kink angle alpha is tuned. No new physical entities are invented.

free parameters (4)
  • gR (critical transverse field of roughening transition) = gR/J ~ 1.38
    Obtained by fitting the BKT correlation length form (Eq. 6) to VUMPS data for Nmax=14; used to place the roughening transition in the phase diagram (Fig. 2d).
  • xi0 and B (BKT fit constants) = not reported
    Non-universal constants in Eq. (6) fitted to extract gR; not used elsewhere.
  • Kink operator angle alpha = alpha = 1.0
    Chosen by hand to maximize agreement between effective and full model dynamics (SM, Kink operator section); the order parameter definition depends on this choice.
  • Bosonic occupation truncation Nmax = Nmax up to 14 (VUMPS); 200 (classical transfer matrix)
    Finite truncation used to approximate the infinite-local-Hilbert-space effective model; gR is extrapolated from Nmax=14 data.
assumptions (6)
  • domain assumption The BKT correlation length divergence form xi(g) = xi0 exp(B/sqrt(|g-gR|)) holds for the effective SOS model.
    Assumed in End Matter to fit gR; standard for BKT but not derived for this model.
  • domain assumption The dynamics is confined to the single-domain-wall subspace (one horizontal interface segment per column, no bubbles/overhangs).
    Basis of Eq. (3); validated only indirectly via Dx/Lx ~ 1 for g/J <= 1.
  • domain assumption Eventual thermalization occurs for g/J >= 0.2, inferred from level spacing statistics of a 4x5 system.
    Footnote 1; used to interpret the slow decay of the imbalance as diffusive thermalization.
  • domain assumption The initial domain wall state has an effective temperature given by the Gibbs state with the same energy (computed by QMC).
    Red line in Fig. 2d; assumes the relevant long-time state is Gibbs-like with the same energy density.
  • domain assumption The bulk and interface contributions to the kink operator factorize so that KM = <K>/<Kbulk>.
    Used for quantitative comparison; stated to be valid only for g/J <= 1.
  • standard math Approximations in Eq. (S12): small q and large Lx limits for the classical transfer matrix result.
    Analytical derivation of TR(Lx), confirmed numerically.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Roughening dynamics of interfaces in the two-dimensional quantum Ising model." pith.science (2026). https://pith.science/paper/KN2DHEHT

@misc{pith2026241210145,
  author       = {Pith},
  title        = {Pith review of: Roughening dynamics of interfaces in the two-dimensional quantum Ising model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KN2DHEHT}},
  note         = {Machine review of arXiv:2412.10145}
}
read the original abstract

The properties of interfaces are key to understand the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale Tree Tensor Network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.

Figures

Figures reproduced from arXiv: 2412.10145 by the authors.

Figure 1
Figure 1. Time evolution of a flat interface on an 8 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a) Mapping from a domain wall state in the full two dimensional model to an effective one-dimensional bosonic [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. (a) Time evolution of the horizontal contribution to [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: a) The energy density and its first two derivatives [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator

    quant-ph 2025-07 conditional novelty 6.0 of 10

    The imbalance decay exponent in a 2D disordered XY model grows with system size, evidence that finite-size 2D many-body localization is unstable, consistent with avalanche delocalization.

  2. Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

    hep-lat 2025-05 conditional novelty 5.0 of 10

    Numerical MPS simulations confirm static roughening signatures in a 2+1D Z2 gauge theory and show that after a local quench the entanglement entropy grows linearly in the roughening region, consistent with a massless ...

Reference graph

Works this paper leans on

64 extracted references · 41 canonical work pages · cited by 2 Pith papers

  1. [1]

    W. K. Burton, N. Cabrera, and F. C. Frank, The growth of crystals and the equilibrium structure of their surfaces, Philosophical Transactions of the Royal Society of Lon- don. Series A, Mathematical and Physical Sciences 243, 299 (1951), publisher: Royal Society

    work page 1951

  2. [2]

    R. L. Dobrushin, Gibbs State Describing Coexistence of Phases for a Three-Dimensional Ising Model, Theory of Probability and Its Applications 17, 582 (1973)

    work page 1973

  3. [3]

    J. D. Weeks, G. H. Gilmer, and H. J. Leamy, Structural Transition in the Ising-Model Interface, Phys. Rev. Lett. 31, 549 (1973)

    work page 1973

  4. [4]

    S. T. Chui and J. D. Weeks, Phase transition in the two- dimensional coulomb gas, and the interfacial roughening transition, Phys. Rev. B 14, 4978 (1976)

    work page 1976

  5. [5]

    van Beijeren, Exactly Solvable Model for the Rough- 6 ening Transition of a Crystal Surface, Physical Review Letters 38, 993 (1977), publisher: American Physical So- ciety

    H. van Beijeren, Exactly Solvable Model for the Rough- 6 ening Transition of a Crystal Surface, Physical Review Letters 38, 993 (1977), publisher: American Physical So- ciety

    work page 1977

  6. [6]

    Hasenbusch, S

    M. Hasenbusch, S. Meyer, and M. P¨ utz, The roughen- ing transition of the three-dimensional Ising interface: A Monte Carlo study, Journal of Statistical Physics 85, 383–401 (1996)

    work page 1996

  7. [7]

    Balibar, H

    S. Balibar, H. Alles, and A. Y. Parshin, The surface of he- lium crystals, Reviews of Modern Physics 77, 317 (2005)

    work page 2005

  8. [8]

    D. S. Fisher and J. D. Weeks, Shape of Crystals at Low Temperatures: Absence of Quantum Roughening, Physi- cal Review Letters 50, 1077 (1983), publisher: American Physical Society

    work page 1983

Show all 64 references
  1. [9]

    Fradkin, Roughening transition in quantum interfaces, Phys

    E. Fradkin, Roughening transition in quantum interfaces, Phys. Rev. B 28, 5338 (1983)

    1983

  2. [10]

    L¨ uscher, Symmetry-breaking aspects of the roughen- ing transition in gauge theories, Nuclear Physics B 180, 317 (1981)

    M. L¨ uscher, Symmetry-breaking aspects of the roughen- ing transition in gauge theories, Nuclear Physics B 180, 317 (1981)

    1981

  3. [11]

    T. A. Cochran et al. , Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories, arXiv:2409.17142 10.48550/arXiv.2409.17142 (2024)

    2024 doi arXiv

  4. [12]

    Kloss, D

    B. Kloss, D. R. Reichman, and Y. B. Lev, Studying dy- namics in two-dimensional quantum lattices using tree tensor network states, SciPost Phys. 9, 070 (2020)

    2020

  5. [13]

    Paveˇ si´ c, D

    L. Paveˇ si´ c, D. Jaschke, and S. Montangero, Constrained dynamics and confinement in the two-dimensional quan- tum Ising model (2024), arXiv:2406.11979

    2024 arXiv

  6. [14]

    Krinitsin, N

    W. Krinitsin, N. Tausendpfund, M. Heyl, M. Rizzi, and M. Schmitt, Time evolution of the quantum ising model in two dimensions using tree tensor networks (2025), arXiv:2505.07612 [quant-ph]

    2025 arXiv

  7. [15]

    Moeckel and S

    M. Moeckel and S. Kehrein, Interaction quench in the hubbard model, Phys. Rev. Lett. 100, 175702 (2008)

    2008

  8. [16]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: a review of exact results, Reports on Progress in Physics 85, 086501 (2022)

    2022

  9. [17]

    Greiner, O

    M. Greiner, O. Mandel, T. W. H¨ ansch, and I. Bloch, Collapse and revival of the matter wave field of a Bose–Einstein condensate, Nature 419, 51–54 (2002)

    2002

  10. [18]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum sim- ulation, Rev. Mod. Phys. 86, 153 (2014)

    2014

  11. [19]

    Kinoshita, T

    T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum Newton’s cradle, Nature 440, 900 (2006)

    2006

  12. [20]

    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, Real-time dynamics of lattice gauge theories with a few-qubit quantum computer, Na- ture 534, 516–519 (2016)

    2016

  13. [21]

    J.-Y. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio- Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Exploring the many-body localization transition in two dimensions, Science 352, 1547 (2016), https://www.science.org/doi/pdf/10.1126/science.aaf8834

    2016 doi

  14. [22]

    Gross and I

    C. Gross and I. Bloch, Quantum simulations with ul- tracold atoms in optical lattices, Science357, 995 (2017), https://www.science.org/doi/pdf/10.1126/science.aal3837

    2017 doi

  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, Direct observation of dynamical quantum phase transitions in an interacting many-body system, Phys. Rev. Lett. 119, 080501 (2017)

    2017

  16. [24]

    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, Nature 551, 579–584 (2017)

    2017

  17. [25]

    Zhang, G

    J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature 551, 601–604 (2017)

    2017

  18. [26]

    G¨ arttner, J

    M. G¨ arttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey, Measuring out- of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet, Nature Physics 13, 781–786 (2017)

    2017

  19. [27]

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, Observation of discrete time-crystalline order in a disor- dered dipolar many-body system, Nature 543, 221–225 (2017)

    2017

  20. [28]

    Levine, A

    H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, High-fidelity control and entanglement of rydberg-atom qubits, Physical Review Letters 121, 10.1103/physrevlett.121.123603 (2018)

    2018 doi

  21. [29]

    S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, and C. Gross, Far-from-equilibrium spin transport in heisenberg quantum magnets, Phys. Rev. Lett. 113, 147205 (2014)

    2014

  22. [30]

    Barredo, V

    D. Barredo, V. Lienhard, S. de L´ es´ eleuc, T. Lahaye, and A. Browaeys, Synthetic three-dimensional atomic structures assembled atom by atom, Nature 561, 79–82 (2018)

    2018

  23. [31]

    Manovitz, S

    T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Koylu- oglu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kali- nowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum coarsening and collective dy-...

    2024 doi arXiv

  24. [32]

    H. W. J. Bl¨ ote and Y. Deng, Cluster Monte Carlo sim- ulation of the transverse Ising model, Phys. Rev. E 66, 066110 (2002)

    2002

  25. [33]

    Balducci, A

    F. Balducci, A. Gambassi, A. Lerose, A. Scardicchio, and C. Vanoni, Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model, Phys. Rev. Lett. 129, 120601 (2022)

    2022

  26. [34]

    Balducci, A

    F. Balducci, A. Gambassi, A. Lerose, A. Scardicchio, and C. Vanoni, Interface dynamics in the two-dimensional quantum Ising model, Phys. Rev. B 107, 024306 (2023)

    2023

  27. [35]

    See Supplemental Material for further details about the tree tensor network simulations, properties of the kink operator, the transfer matrix analysis, and the quantum Monte Carlo simulations

  28. [36]

    Silvi, F

    P. Silvi, F. Tschirsich, M. Gerster, J. J¨ unemann, D. Jaschke, M. Rizzi, and S. Montangero, The Tensor Networks Anthology: Simulation techniques for many- body quantum lattice systems, SciPost Phys. Lect. Notes , 8 (2019)

    2019

  29. [37]

    Haegeman, J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Ver- schelde, and F. Verstraete, Time-dependent variational principle for quantum lattices, Phys. Rev. Lett. 107, 070601 (2011)

    2011

  30. [38]

    Haegeman, C

    J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, Unifying time evolution and optimiza- 7 tion with matrix product states, Phys. Rev. B94, 165116 (2016)

    2016

  31. [39]

    Zauner-Stauber, L

    V. Zauner-Stauber, L. Vanderstraeten, M. T. Fishman, F. Verstraete, and J. Haegeman, Variational optimization algorithms for uniform matrix product states, Phys. Rev. B 97, 045145 (2018)

    2018

  32. [40]

    H. G. Evertz, G. Lana, and M. Marcu, Cluster algorithm for vertex models, Phys. Rev. Lett. 70, 875 (1993)

    1993

  33. [41]

    H. G. Evertz, The loop algorithm, Advances in Physics 52, 1–66 (2003)

    2003

  34. [42]

    Yueh and S

    W.-C. Yueh and S. S. Cheng, Explicit eigenvalues and inverses of tridiagonal toeplitz matrices with four per- turbed corners, The ANZIAM Journal 49, 361–387 (2008)

    2008

  35. [43]

    A. A. Abul-Magd and A. Y. Abul-Magd, Unfolding of the spectrum for chaotic and mixed systems, Physica A: Statistical Mechanics and its Applications 396, 185–194 (2014)

    2014

  36. [44]

    Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Distribution of the ratio of consecutive level spacings in random matrix ensembles, Physical Review Letters 110, 10.1103/physrevlett.110.084101 (2013)

    2013 doi

  37. [45]

    Sachdev, Quantum Phase Transitions , 2nd ed

    S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cam- bridge University Press, 2011)

    2011

  38. [46]

    Fradkin and L

    E. Fradkin and L. Susskind, Order and disorder in gauge systems and magnets, Physical Review D 17, 2637 (1978)

    1978

  39. [47]

    Hasenfratz, E

    A. Hasenfratz, E. Hasenfratz, and P. Hasenfratz, Gener- alized roughening transition and its effect on the string tension, Nuclear Physics B 180, 353 (1981)

    1981

  40. [48]

    S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Continuous quantum phase transitions, Rev. Mod. Phys. 69, 315 (1997)

    1997

  41. [49]

    Hasenbusch, The two-dimensional XY model at the transition temperature: a high-precision Monte Carlo study, Journal of Physics A: Mathematical and General 38, 5869 (2005)

    M. Hasenbusch, The two-dimensional XY model at the transition temperature: a high-precision Monte Carlo study, Journal of Physics A: Mathematical and General 38, 5869 (2005)

    2005

  42. [50]

    J. A. Cuesta and A. S´ anchez, General non-existence the- orem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions, Journal of Statistical Physics 115, 869–893 (2004)

    2004

  43. [51]

    Zeiher, J.-y

    J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Coherent Many-Body Spin Dynamics in a Long-Range Interacting Ising Chain, Physical Review X 7, 041063 (2017), arXiv:1705.08372 [physics.atom-ph]

    2017 arXiv

  44. [52]

    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, Nature 551, 579 (2017)

    2017

  45. [53]

    Scholl, M

    P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L¨ auchli, and A. Browaeys, Quantum simulation of 2d antiferromagnets with hun- dreds of rydberg atoms, Nature 595, 233–238 (2021)

    2021

  46. [54]

    Coleman, Fate of the false vacuum: Semiclassical the- ory, Phys

    S. Coleman, Fate of the false vacuum: Semiclassical the- ory, Phys. Rev. D 15, 2929 (1977)

    1977

  47. [55]

    Lagnese, F

    G. Lagnese, F. M. Surace, M. Kormos, and P. Calabrese, False vacuum decay in quantum spin chains, Phys. Rev. B 104, L201106 (2021)

    2021

  48. [56]

    Milsted, J

    A. Milsted, J. Liu, J. Preskill, and G. Vidal, Collisions of false-vacuum bubble walls in a quantum spin chain, PRX Quantum 3, 020316 (2022)

    2022

  49. [57]

    Zenesini, A

    A. Zenesini, A. Berti, R. Cominotti, C. Rogora, I. G. Moss, T. P. Billam, I. Carusotto, G. Lamporesi, A. Re- cati, and G. Ferrari, False vacuum decay via bubble for- mation in ferromagnetic superfluids, Nature Physics 20, 558 (2024)

    2024

  50. [58]

    Tausendpfund, M

    N. Tausendpfund, M. Rizzi, W. Krinitsin, and M. Schmitt, TTN – A tree tensor network library for cal- culating groundstates and solving time evolution (2024), available on Zenodo

    2024

  51. [59]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calcula- tions, SciPost Phys. Codebases , 4 (2022)

    2022

  52. [60]

    Bauer, L

    B. Bauer, L. D. Carr, H. G. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler, A. Hehn, R. Igarashi, S. V. Isakov, D. Koop, P. N. Ma, P. Mates, H. Matsuo, O. Parcol- let, G. Paw/suppress lowski, J. D. Picon, L. Pollet, E. Santos, V. W. Sc...

    2011

  53. [61]

    J¨ ulich Supercomputing Centre, JUWELS Cluster and Booster: Exascale Pathfinder with Modular Supercom- puting Architecture at JSC, Journal of large-scale re- search facilities 7, A183 (2021)

    2021

  54. [62]

    J¨ ulich Supercomputing Centre, JURECA: Data Centric and Booster Modules implementing the Modular Super- computing Architecture at JSC, Journal of large-scale research facilities 7, A182 (2021)

    2021

  55. [63]

    Roughening dynamics of interfaces in two-dimensional quantum matter

    W. Krinitsin, N. Tausendpfund, M. Rizzi, M. Heyl, and M. Schmitt, Data and code associated to the paper “Roughening dynamics of interfaces in two-dimensional quantum matter”, 10.5281/zenodo.14705609 (2025)

    2025 doi

  56. [64]

    ROUGHENING DYNAMICS OF INTERFACES IN THE TWO-DIMENSIONAL QUANTUM ISING MODEL

    S. Hearth, IsingMonteCarlo (2024). End Matter BKT transition of the SOS Model. In this paragraph, we demonstrate that the nature of the transition in the effective SOS model (3) belongs to the BKT universality class. To this end, we use the VUMPS algorithm [37– 39] to study th...

    2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.