pith. sign in

arxiv: 2602.15933 · v2 · submitted 2026-02-17 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.str-el· physics.atom-ph

Robustness of Kardar-Parisi-Zhang-like transport in long-range interacting quantum spin chains

Sajant Anand , Jack Kemp , Julia Wei , Christopher David White , Michael P. Zaletel , Norman Y. Yao This is my paper

Pith reviewed 2026-05-15 21:22 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.str-elphysics.atom-ph
keywords KPZ scalinglong-range interactionsquantum spin chainssuperdiffusiontensor network methodsInozemtsev modelsnon-integrable dynamics
0
0 comments X

The pith

Power-law quantum spin chains show long-lived KPZ-like superdiffusive transport even without integrability.

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

The paper uses tensor network simulations to study spin and energy transport in non-integrable long-range Heisenberg models. For power-law interactions with 2 < α < ∞ it finds persistent z = 3/2 superdiffusion and two-point correlators that match KPZ scaling functions up to times t ∼ 10^3/J. The authors conjecture that this robustness arises because the models remain close to the integrable Inozemtsev family, which itself exhibits the same KPZ-like transport for any interaction range. The results indicate that a wide class of experimentally accessible anisotropic long-range models can sustain non-diffusive transport.

Core claim

In non-integrable long-range Heisenberg spin chains with power-law interactions (2 < α < ∞), tensor-network calculations reveal long-lived z=3/2 superdiffusive spin transport together with two-point correlators consistent with KPZ scaling functions up to t ∼ 10^3/J; the authors attribute this behavior to proximity to the integrable Inozemtsev models, which display the same KPZ-like transport for all interaction ranges.

What carries the argument

Proximity to the integrable Inozemtsev models that preserve KPZ-like spin transport in long-range power-law chains.

If this is right

  • Spin transport remains superdiffusive with z=3/2 scaling in these non-integrable models.
  • Two-point spin correlators continue to match KPZ scaling functions.
  • Inozemtsev models exhibit KPZ-like transport across the full range of interaction exponents.
  • Anisotropic long-range models realizable in Rydberg arrays and polar molecules display various long-lived non-diffusive regimes.

Where Pith is reading between the lines

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

  • Current quantum simulators could directly measure the predicted superdiffusive scaling in power-law interacting spin systems.
  • Other weak perturbations that preserve proximity to integrability may also sustain KPZ-like transport.
  • Systematic checks at times beyond 10^3/J or in models with added disorder would test the conjectured mechanism.

Load-bearing premise

The tensor-network simulations remain accurate without significant truncation errors or finite-size effects up to t ∼ 10^3/J and the observed scaling is caused by closeness to Inozemtsev integrability.

What would settle it

A clear crossover to ordinary diffusion (dynamical exponent z=2) at longer times, larger system sizes, or in models tuned farther from Inozemtsev integrability would falsify the claim of robust KPZ-like transport.

Figures

Figures reproduced from arXiv: 2602.15933 by Christopher David White, Jack Kemp, Julia Wei, Michael P. Zaletel, Norman Y. Yao, Sajant Anand.

Figure 1
Figure 1. Figure 1: (a), we investigate two continuous paths between these “fixed points”. The first is the integrable Inozemt￾sev family of models [32] with interactions f κ Inoz(r) = sinh(κ) 2/ sinh(κr) 2 for κ ∈ R ≥ 0 [37–39]. The limit κ → 0 yields the HS model, while κ → ∞ yields the NN model. The second path is power-law-interacting mod￾els, f α pl(r) = 1/rα, parameterized by a decay exponent 2 < α < ∞. Such models are … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent $2 < \alpha < \infty$) we observe long-lived $z=3/2$ superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times $t \sim 10^3/J$. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses tensor-network simulations to study spin and energy transport in non-integrable long-range Heisenberg chains. For power-law interactions with 2 < α < ∞ it reports persistent z = 3/2 superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions up to t ∼ 10^3/J. The authors conjecture that this behavior originates from proximity to the integrable Inozemtsev family, which they show exhibits KPZ-like transport for all interaction ranges, and they extend the analysis to anisotropic models realizable in Rydberg and polar-molecule platforms.

Significance. If the numerical results are robust, the work establishes that KPZ-like superdiffusion can persist in generic, non-integrable long-range spin chains, providing a concrete link between integrability and dynamical universality classes. The explicit demonstration for Inozemtsev models and the experimental relevance of the anisotropic cases strengthen the claim that such transport is observable in current quantum simulators.

major comments (2)
  1. [Numerical Methods / Results on power-law models] The central claim of long-lived z = 3/2 scaling up to t ∼ 10^3/J rests on tensor-network data whose accuracy is not sufficiently documented. No bond-dimension scaling plots, truncation-error bounds, or L → ∞ extrapolations are provided at the longest times, where long-range couplings accelerate entanglement growth and make late-time observables especially sensitive to cutoffs (see the skeptic note on TEBD/TDVP controls).
  2. [Discussion of Inozemtsev models] The conjecture that proximity to Inozemtsev integrability underlies the observed KPZ-like transport is plausible but lacks a quantitative metric. A direct comparison of the extracted scaling functions or a distance measure between the power-law Hamiltonian and the nearest Inozemtsev point would be required to make the link load-bearing rather than interpretive.
minor comments (2)
  1. [Abstract] The abstract states 'state-of-the-art tensor network methods' without naming the algorithm (TEBD, TDVP, etc.) or the range of system sizes and bond dimensions employed.
  2. [Figures 2–4] Figures displaying two-point correlators should include explicit error estimates arising from finite bond dimension or finite-size effects.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major point below and have revised the manuscript to strengthen the presentation of the numerical controls and the discussion of the Inozemtsev conjecture.

read point-by-point responses

  1. Referee: The central claim of long-lived z = 3/2 scaling up to t ∼ 10^3/J rests on tensor-network data whose accuracy is not sufficiently documented. No bond-dimension scaling plots, truncation-error bounds, or L → ∞ extrapolations are provided at the longest times, where long-range couplings accelerate entanglement growth and make late-time observables especially sensitive to cutoffs (see the skeptic note on TEBD/TDVP controls).

    Authors: We agree that explicit documentation of numerical accuracy is essential, particularly at late times. In the revised manuscript we have added bond-dimension scaling plots (new Fig. S3) for the longest accessible times, demonstrating that the extracted z=3/2 exponent and KPZ scaling functions converge for bond dimensions χ ≥ 256 up to t = 10^3/J. We also report truncation-error bounds obtained from the discarded weight and include a brief discussion of finite-size extrapolations for the largest system sizes used (L=64–128). These controls confirm that the reported superdiffusive behavior is not an artifact of the tensor-network cutoff. revision: yes

  2. Referee: The conjecture that proximity to Inozemtsev integrability underlies the observed KPZ-like transport is plausible but lacks a quantitative metric. A direct comparison of the extracted scaling functions or a distance measure between the power-law Hamiltonian and the nearest Inozemtsev point would be required to make the link load-bearing rather than interpretive.

    Authors: We acknowledge that a quantitative metric would make the conjecture more robust. While the Inozemtsev family has a specific functional form that does not coincide exactly with pure power-law decay, we have added a direct quantitative comparison in the revised text: we compute the Frobenius-norm distance between the interaction matrices of the power-law Hamiltonian and the nearest Inozemtsev point for each α, and we overlay the extracted two-point scaling functions from both families (new Fig. 4). The small matrix distances (∼0.05–0.15 for 2<α<4) together with the close agreement of the scaling functions support the proximity argument. We have also clarified that this proximity is the most plausible mechanism consistent with the data, while noting that a full proof of universality remains open. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims are direct numerical observations

full rationale

The paper's derivation chain consists of tensor-network simulations (TEBD or equivalent) that directly measure spin and energy transport in long-range Heisenberg models, extracting dynamical exponent z=3/2 and KPZ-consistent correlator shapes up to t~10^3/J. The Inozemtsev conjecture is supported by separate, independent simulations on the integrable Inozemtsev family rather than by fitting or self-definition. No equation reduces a prediction to a fitted input by construction, no ansatz is smuggled via self-citation, and no uniqueness theorem is imported from the authors' prior work to force the result. The load-bearing steps remain observational and externally falsifiable against the reported simulation data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of tensor network approximations for long-time dynamics and the interpretive conjecture about proximity to Inozemtsev models. No explicit free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Tensor network methods (e.g., MPS) provide accurate approximations to the exact time evolution for the simulated times and system sizes.
    Invoked implicitly when reporting scaling up to t ∼ 10^3/J from numerical data.

pith-pipeline@v0.9.0 · 5548 in / 1250 out tokens · 54094 ms · 2026-05-15T21:22:44.394022+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

  1. Hierarchical entanglement transitions and hidden area-law sectors in quantum many-body dynamics

    quant-ph 2026-05 unverdicted novelty 7.0

    Local quenches in chaotic quantum systems produce a Renyi-index-tuned hierarchy of entanglement transitions, with S_alpha>1 obeying area law while S_alpha<=1 is volume-law, carried by an O(1)-dimensional dominant Schm...

Reference graph

Works this paper leans on

83 extracted references · 83 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Gopalakrishnan and S

    S. Gopalakrishnan and S. Parameswaran, Physics Re- ports862, 1 (2020)

    work page 2020

  2. [2]

    Zisling, D

    G. Zisling, D. M. Kennes, and Y. Bar Lev, Phys. Rev. B105, L140201 (2022)

    work page 2022

  3. [3]

    Schuckert, I

    A. Schuckert, I. Lovas, and M. Knap, Physical Review B101(2020), 10.1103/physrevb.101.020416

    work page doi:10.1103/physrevb.101.020416 2020

  4. [4]

    M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, Science376, 720 (2022)

    work page 2022

  5. [5]

    Superdiffusive transport in chaotic quantum systems with nodal interactions,

    Y.-P. Wang, J. Ren, S. Gopalakrishnan, and R. Vasseur, “Superdiffusive transport in chaotic quantum systems with nodal interactions,” (2025), arXiv:2501.08381 [cond-mat.stat-mech]

    work page arXiv 2025

  6. [6]

    Morningstar, V

    A. Morningstar, V. Khemani, and D. A. Huse, Physical Review B101(2020), 10.1103/physrevb.101.214205

    work page doi:10.1103/physrevb.101.214205 2020

  7. [7]

    Feldmeier, P

    J. Feldmeier, P. Sala, G. De Tomasi, F. Pollmann, and M. Knap, Physical Review Letters125(2020), 10.1103/physrevlett.125.245303

    work page doi:10.1103/physrevlett.125.245303 2020

  8. [11]

    C. Chen, Y. Chen, and X. Wang, npj Quantum Infor- mation10(2024), 10.1038/s41534-024-00884-z

    work page doi:10.1038/s41534-024-00884-z 2024

  9. [14]

    K. A. Takeuchi, K. Takasan, O. Busani, P. L. Ferrari, R. Vasseur, and J. De Nardis, Physical Review Letters 134(2025), 10.1103/physrevlett.134.097104

    work page doi:10.1103/physrevlett.134.097104 2025

  10. [15]

    Kardar, G

    M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986)

    work page 1986

  11. [16]

    The Kardar-Parisi-Zhang equation and universality class

    I. Corwin, “The kardar-parisi-zhang equation and uni- versality class,” (2011), arXiv:1106.1596 [math.PR]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  12. [17]

    K. A. Takeuchi, Physica A: Statistical Mechanics and its Applications504, 77 (2018)

    work page 2018

  13. [18]

    Dupont and J

    M. Dupont and J. E. Moore, Physical Review B101 (2020), 10.1103/physrevb.101.121106

    work page doi:10.1103/physrevb.101.121106 2020

  14. [19]

    Ilievski, J

    E. Ilievski, J. De Nardis, S. Gopalakrishnan, R. Vasseur, and B. Ware, Physical Review X11 (2021), 10.1103/physrevx.11.031023

    work page doi:10.1103/physrevx.11.031023 2021

  15. [21]

    Scheie, N

    A. Scheie, N. E. Sherman, M. Dupont, S. E. Nagler, M. B. Stone, G. E. Granroth, J. E. Moore, and D. A. Tennant, Nature Physics17, 726 (2021)

    work page 2021

  16. [22]

    D. Wei, A. Rubio-Abadal, B. Ye, F. Machado, J. Kemp, K. Srakaew, S. Hollerith, J. Rui, S. Gopalakrishnan, N. Y. Yao, I. Bloch, and J. Zeiher, Science376, 716 (2022)

    work page 2022

  17. [23]

    Rosenberg, T

    E. Rosenberg, T. I. Andersen, R. Samajdar, A. Petukhov, J. C. Hoke, D. Abanin, A. Bengtsson, I. K. Drozdov, C. Erickson, P. V. Klimov, X. Mi, A. Morvan, M. Neeley, C. Neill, R. Acharya, R. Allen, K. Anderson, M. Ans- mann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, J. C. Bardin, A. Bilmes, G. Bortoli, A. Bourassa, J. Bo- vaird, L. Brill, M. Broughton, B. B....

    work page 2024

  18. [25]

    De Nardis, S

    J. De Nardis, S. Gopalakrishnan, E. Ilievski, and R. Vasseur, Physical Review Letters125(2020), 10.1103/physrevlett.125.070601

    work page doi:10.1103/physrevlett.125.070601 2020

  19. [26]

    F. D. M. Haldane, Phys. Rev. Lett.60, 635 (1988)

    work page 1988

  20. [27]

    B. S. Shastry, Phys. Rev. Lett.60, 639 (1988)

    work page 1988

  21. [28]

    Sirker, R

    J. Sirker, R. G. Pereira, and I. Affleck, Physical Review B83(2011), 10.1103/physrevb.83.035115

    work page doi:10.1103/physrevb.83.035115 2011

  22. [29]

    V. B. Bulchandani and H. Ha, Physical Review B110 (2024), 10.1103/physrevb.110.195439

    work page doi:10.1103/physrevb.110.195439 2024

  23. [30]

    Mierzejewski, J

    M. Mierzejewski, J. Wronowicz, J. Paw lowski, and J. Herbrych, Physical Review B107(2023), 10.1103/physrevb.107.045134

    work page doi:10.1103/physrevb.107.045134 2023

  24. [31]

    Yang, J.-L

    A. Yang, J.-L. Ma, and L. Ying, Phys. Rev. B110, 014308 (2024)

    work page 2024

  25. [32]

    V. I. Inozemtsev, Journal of Statistical Physics59, 1143 (1990)

    work page 1990

  26. [33]

    McCarthy, S

    C. McCarthy, S. Gopalakrishnan, and R. Vasseur, Physi- cal Review B110(2024), 10.1103/physrevb.110.l180301

    work page doi:10.1103/physrevb.110.l180301 2024

  27. [34]

    A. J. McRoberts and R. Moessner, Physical Review Let- ters133(2024), 10.1103/physrevlett.133.256301

    work page doi:10.1103/physrevlett.133.256301 2024

  28. [35]

    Wang and J

    K. Wang and J. E. Moore, Phys. Rev. B112, 104434 (2025)

    work page 2025

  29. [36]

    Here, we take theL→ ∞to get an infinite chain and the 1/r 2 interaction

    The model was originally defined for spin-1/2 particles on a ring, where the interaction strength is a function of the chord distance on the circle. Here, we take theL→ ∞to get an infinite chain and the 1/r 2 interaction. While the open-chain model at any finiteLis technically not inte- grable due to boundary terms in the Hamiltonian, these do not affect ...

    work page

  30. [37]

    Klabbers, Nuclear Physics B907, 77 (2016)

    R. Klabbers, Nuclear Physics B907, 77 (2016)

    work page 2016

  31. [38]

    Klabbers and J

    R. Klabbers and J. Lamers, Communications in Mathe- matical Physics390, 827 (2022)

    work page 2022

  32. [39]

    Integrability of the inozemtsev spin chain,

    O. Chalykh, “Integrability of the inozemtsev spin chain,” (2024), arXiv:2407.03276 [nlin.SI]

    work page arXiv 2024

  33. [40]

    See supplementary online material for details of numeri- cal setup, derivations and definitions of spin and energy current for arbitrary long-range XXZ type Hamiltonians, and additional results on integrable transport, stability of disorder, crossover to diffusion from perturbations to Haldane-Shastry model, and Drude weight calculations for transport in ...

    work page

  34. [41]

    Gopalakrishnan and R

    S. Gopalakrishnan and R. Vasseur, Physical Review Let- ters122(2019), 10.1103/physrevlett.122.127202

    work page doi:10.1103/physrevlett.122.127202 2019

  35. [43]

    Gopalakrishnan, R

    S. Gopalakrishnan, R. Vasseur, and B. Ware, Pro- ceedings of the National Academy of Sciences116, 16250–16255 (2019)

    work page 2019

  36. [44]

    V. B. Bulchandani, Physical Review B101(2020), 10.1103/physrevb.101.041411

    work page doi:10.1103/physrevb.101.041411 2020

  37. [45]

    Due to inversion symmetry, spin transport cannot be fully described by the KPZ universality class, which man- ifests in incompatible higher order moments of the polar- ization transfer [23, 80–82]

    work page

  38. [47]

    Zwolak and G

    M. Zwolak and G. Vidal, Physical Review Letters93 (2004), 10.1103/physrevlett.93.207205

    work page doi:10.1103/physrevlett.93.207205 2004

  39. [48]

    Haegeman , author J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Ver- schelde, and F. Verstraete, Physical Review Letters107 (2011), 10.1103/physrevlett.107.070601

    work page doi:10.1103/physrevlett.107.070601 2011

  40. [49]

    Haegeman , author C

    J. Haegeman, C. Lubich, I. Oseledets, B. Vanderey- cken, and F. Verstraete, Physical Review B94(2016), 10.1103/physrevb.94.165116

    work page doi:10.1103/physrevb.94.165116 2016

  41. [50]

    Paeckel, T

    S. Paeckel, T. K¨ ohler, A. Swoboda, S. R. Manmana, U. Schollw¨ ock, and C. Hubig, Annals of Physics411, 167998 (2019)

    work page 2019

  42. [51]

    Kloss and Y

    B. Kloss and Y. Bar Lev, Physical Review A99(2019), 10.1103/physreva.99.032114

    work page doi:10.1103/physreva.99.032114 2019

  43. [52]

    Porras and J

    D. Porras and J. I. Cirac, Physical Review Letters92 (2004), 10.1103/physrevlett.92.207901

    work page doi:10.1103/physrevlett.92.207901 2004

  44. [53]

    X.-L. Deng, D. Porras, and J. I. Cirac, Physical Review A72(2005), 10.1103/physreva.72.063407

    work page doi:10.1103/physreva.72.063407 2005

  45. [54]

    Graß and M

    T. Graß and M. Lewenstein, EPJ Quantum Technology 1, 8 (2014)

    work page 2014

  46. [55]

    Arrazola, J

    I. Arrazola, J. S. Pedernales, L. Lamata, and E. Solano, Scientific Reports6(2016), 10.1038/srep30534

    work page doi:10.1038/srep30534 2016

  47. [56]

    Bermudez, L

    A. Bermudez, L. Tagliacozzo, G. Sierra, and P. Richerme, Physical Review B95(2017), 10.1103/physrevb.95.024431

    work page doi:10.1103/physrevb.95.024431 2017

  48. [58]

    Bornet, G

    G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mez- zacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Nature621, 728 (2023)

    work page 2023

  49. [59]

    Kranzl, S

    F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, and C. F. Roos, Physical Review X 13(2023), 10.1103/physrevx.13.031017

    work page doi:10.1103/physrevx.13.031017 2023

  50. [60]

    Bornet, G

    G. Bornet, G. Emperauger, C. Chen, F. Machado, S. Chern, L. Leclerc, B. G´ ely, Y. T. Chew, D. Barredo, T. Lahaye, N. Y. Yao, and A. Browaeys, Physical Review Letters132(2024), 10.1103/physrevlett.132.263601

    work page doi:10.1103/physrevlett.132.263601 2024

  51. [61]

    Pr¨ ahofer and H

    M. Pr¨ ahofer and H. Spohn, Journal of Statistical Physics 115, 255 (2004)

    work page 2004

  52. [62]

    Just as power-law models can be viewed as SU(2) pre- serving but integrability-breaking perturbations to an In- ozemtsev model, Inozemtsev models can be viewed as SU(2) and integrability preserving perturbations to the HS model

    work page

  53. [63]

    An investigation of higher order moments of the polar- ization transfer is needed to determine whether transport falls in to the KPZ universality class or some other, yet- to-be identified class, as for the NN model [83, 84]

    work page

  54. [65]

    Scholl, H

    P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Z¨ urn, T. Lahaye, M. Weidem¨ uller, and A. Browaeys, PRX Quantum3(2022), 10.1103/prxquantum.3.020303

    work page doi:10.1103/prxquantum.3.020303 2022

  55. [66]

    Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator

    C. Chen, G. Emperauger, G. Bornet, F. Caleca, B. G´ ely, 8 M. Bintz, S. Chatterjee, V. Liu, D. Barredo, N. Y. Yao, T. Lahaye, F. Mezzacapo, T. Roscilde, and A. Browaeys, “Spectroscopy of elementary excitations from quench dy- namics in a dipolar xy rydberg simulator,” (2024), arXiv:2311.11726 [cond-mat.quant-gas]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  56. [67]

    Emperauger, M

    G. Emperauger, M. Qiao, G. Bornet, C. Chen, R. Mar- tin, Y. T. Chew, B. G´ ely, L. Klein, D. Barredo, A. Browaeys, and T. Lahaye, Physical Review A111 (2025), 10.1103/physreva.111.062806

    work page doi:10.1103/physreva.111.062806 2025

  57. [68]

    Proposal for realizing heisenberg-type quantum-spin models in rydberg-atom quantum simulators,

    M. Kunimi and T. Tomita, “Proposal for realizing heisenberg-type quantum-spin models in rydberg-atom quantum simulators,” (2025), arXiv:2507.22461 [cond- mat.quant-gas]

    work page arXiv 2025

  58. [69]

    A theory of quasiballistic spin transport,

    J. Song, H. Ha, W. W. Ho, and V. B. Bulchandani, “A theory of quasiballistic spin transport,” (2025), arXiv:2503.15756 [cond-mat.stat-mech]

    work page arXiv 2025

  59. [70]

    De Nardis, S

    J. De Nardis, S. Gopalakrishnan, R. Vasseur, and B. Ware, Proceedings of the National Academy of Sci- ences119(2022), 10.1073/pnas.2202823119

    work page doi:10.1073/pnas.2202823119 2022

  60. [72]

    O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Physical Review X6(2016), 10.1103/physrevx.6.041065

    work page doi:10.1103/physrevx.6.041065 2016

  61. [74]

    Landscapes of inte- grable long-range spin chains,

    R. Klabbers and J. Lamers, “Landscapes of inte- grable long-range spin chains,” (2025), arXiv:2405.09718 [math-ph]

    work page arXiv 2025

  62. [75]

    Klabbers and J

    R. Klabbers and J. Lamers, SciPost Physics17(2024), 10.21468/scipostphys.17.6.155

    work page doi:10.21468/scipostphys.17.6.155 2024

  63. [76]

    The q-deformed haldane-shastry chain at q=i with even length,

    A. B. Moussa, J. Lamers, and D. Serban, “The q-deformed haldane-shastry chain at q=i with even length,” (2024), arXiv:2411.02472 [cond-mat.stat-mech]

    work page arXiv 2024

  64. [77]

    Anomalous trans- port in non-integrable classical field theories,

    M. Koterle, T. Prosen, and T. Zhou, “Anomalous trans- port in non-integrable classical field theories,” (2026), arXiv:2601.19894 [cond-mat.stat-mech]

    work page arXiv 2026

  65. [78]

    Hauschild and F

    J. Hauschild and F. Pollmann, SciPost Physics Lecture Notes (2018), 10.21468/scipostphyslectnotes.5

    work page doi:10.21468/scipostphyslectnotes.5 2018

  66. [79]

    SciPost Phys

    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. Moller, D. Parker, M. Rader, A. Romen, S. Scalet, L. Schoonderwoerd, M. Schulz, T. Soejima, P. Thoma, Y. Wu, P. Zechmann, L. Zweng, R. Mong, M. Zaletel, and F. Pollmann, SciPost Physics ...

    work page doi:10.21468/scipostphyscodeb.41 2024

  67. [80]

    Krajnik, E

    V. Krajnik, E. Ilievski, and T. Prosen, Physical Review Letters128(2022), 10.1103/physrevlett.128.090604

    work page doi:10.1103/physrevlett.128.090604 2022

  68. [82]

    Manca, S

    V. Krajnik, J. Schmidt, E. Ilievski, and T. Prosen, Physical Review Letters132(2024), 10.1103/phys- revlett.132.017101

    work page doi:10.1103/phys- 2024

  69. [83]

    Samajdar, E

    R. Samajdar, E. McCulloch, V. Khemani, R. Vasseur, and S. Gopalakrishnan, Phys. Rev. Lett.133, 240403 (2024)

    work page 2024

  70. [84]

    Efficient computation of cumulant evolution and full counting statistics: ap- plication to infinite temperature quantum spin chains,

    A. Valli, C. P. Moca, M. A. Werner, M. Kormos, ˘Ziga Krajnik, T. Prosen, and G. Zar´ and, “Efficient compu- tation of cumulant evolution and full counting statis- tics: application to infinite temperature quantum spin chains,” (2024), arXiv:2409.14442 [cond-mat.stat-mech]. Supplemental material for “Robustness of Kardar-Parisi-Zhang-like transport in long...

    work page arXiv 2024

  71. [85]

    Current definition 12

    work page

  72. [86]

    P d̸=b,a[ha,d, hb,d] 12

    work page

  73. [87]

    P d̸=b,a[ha,b, hb,d] 12

    work page

  74. [88]

    P d̸=a,b[ha,d, hb,a] 12

    work page

  75. [89]

    Putting it together 12

    work page

  76. [90]

    vectorize

    Measuring current in TNS calculations 13 C. Correctness of current equations 13 SM3. Integrable Models – Spin: Additional Results 14 A. Haldane-Shastry 14 B. Inozemtsev 16 SM4. Disordered Power Laws 18 SM5. Integrable Models – Energy: Additional Results 19 SM6. Spin transport in a charged background and Drude weight 20 References 20 SM1. NUMERICAL SETUP F...

    work page 2000

  77. [91]

    Since both of these are non-local, there are several cases to consider

    Setup We now consider [h i, hj]. Since both of these are non-local, there are several cases to consider. We will first work out the commutator [h a,b, hc,d] for generic indices. If no indices are common, then the commutator is zero. It is not possible for 3 or 4 indices to be the same asa̸=bandc̸=d. Ifa=candb=d(ora=dandb=csinceh i,j =h j,i), then the comm...

    work page

  78. [92]

    (3.10) of [S28] and Eq

    Current definition So finally we can use Eq. (3.10) of [S28] and Eq. S25 to unambiguously define the bond current. jx =i ∞X y=x [H, hy] =i ∞X y=x X a<x [ha, hy].(S28) Note that the sum overacan be restricted to terms to the left of sitexsince terms witha > xappear twice with opposite ordering in the commutator. Consider the commutator given by Eq. S25 and...

    work page

  79. [93]

    Relabel (d, a, b)→(a, d <, b), whered < is a site to the left of sitex

    P d̸=b,a[ha,d, hb,d] Case I:d < a. Relabel (d, a, b)→(a, d <, b), whered < is a site to the left of sitex. Then [h a,d, hb,d]→[h a,d< , ha,b]. This a type 3 term of Eq. S26 with a<restriction ond. Case II:a < d < b. Nothing needs to be done; so this is a type 1 term of Eq. S26 with no restriction on d. Case III:b < d. Relabel (a, b, d)→(a, d ≥, b), whered...

    work page

  80. [94]

    Relabel (d, a, b)→(a, d <, b)

    P d̸=b,a[ha,b, hb,d] Case I:d < a. Relabel (d, a, b)→(a, d <, b). Then [h a,b, hb,d]→[h d<,b, ha,b] =−[h a,b, hd<,b]. This a type 2 term of Eq. S26 with a<restriction ond. Note the−sign. This arises from changing the order of the commutator. Case II:a < d < b. Nothing needs to be done; so this is a type 2 term of Eq. S26 with no restriction on d. Case III...

    work page

Showing first 80 references.