Pith. sign in

REVIEW 2 major objections 2 minor 51 references

KPZ dynamics emerges in the B3 open integrable model rather than diffusion from the spontaneous symmetry breaking ansatz.

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

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

T0 review · grok-4.3

2026-07-03 11:48 UTC pith:EU436MHE

load-bearing objection The paper maps the B3 model to two asymmetric XXZ chains and shows KPZ scaling can dominate over the SSB ansatz for chosen initial states. the 2 major comments →

arxiv 2607.02341 v1 pith:EU436MHE submitted 2026-07-02 quant-ph

Kardar-Parisi-Zhang dynamics in an open integrable system: beyond the spontaneous-symmetry-breaking ansatz

Guo-Qiang Wang , Chang-Ling Zou , Guang-Can Guo , and Xu-Bo Zou This is my paper
classification quant-ph
keywords Kardar-Parisi-Zhang dynamicsopen quantum systemsintegrable systemsXXZ spin chainsspontaneous symmetry breakingcharge transporthydrodynamicsnon-equilibrium dynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper investigates whether a spontaneous symmetry breaking ansatz fully describes charge transport in open quantum systems. In the B3 model, the authors find that the dynamics map to two asymmetric XXZ spin chains. The ansatz only handles the interactions between these chains, while the asymmetry within chains can produce KPZ scaling for suitable initial states. This occurs even when the hopping rate is negative. The finding indicates that transport theories in open systems need to go beyond the symmetry breaking picture.

Core claim

The B3 model is equivalent to two interacting asymmetric XXZ spin chains, and when the asymmetric XXZ structure dominates, it gives rise to KPZ scaling behavior instead of the diffusion expected from the spontaneous symmetry breaking ansatz.

What carries the argument

Equivalence of the B3 model to two interacting asymmetric XXZ spin chains, where the intra-chain asymmetry drives the KPZ dynamics beyond inter-chain effects captured by the ansatz.

Load-bearing premise

The B3 model can be treated as two interacting asymmetric XXZ spin chains whose asymmetry dominates the dynamics for chosen initial states.

What would settle it

Direct simulation or measurement showing that the dynamical exponent remains 2 (diffusive) rather than 3/2 (KPZ) in the B3 model with negative hopping and appropriate initial states would disprove the emergence of KPZ dynamics.

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

If this is right

  • KPZ scaling persists in the model with negative hopping rates under appropriate initial conditions.
  • The spontaneous symmetry breaking ansatz misses the contribution from asymmetric chain structures.
  • Hydrodynamic descriptions of open integrable systems must account for such asymmetries.
  • Charge transport can exhibit superdiffusive behavior in these setups.

Where Pith is reading between the lines

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

  • Similar mappings might reveal KPZ or other scalings in additional open quantum models.
  • Experimental realizations could use the B3 model to observe KPZ without relying on symmetry breaking.
  • This approach might connect to studies of non-equilibrium dynamics in quantum chains.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript claims that Kardar-Parisi-Zhang (KPZ) dynamics, rather than diffusion from the spontaneous symmetry breaking (SSB) ansatz, emerges in the open integrable B3 model. It establishes that the B3 model is equivalent to two interacting asymmetric XXZ spin chains, with the SSB ansatz capturing only the inter-chain interactions; for appropriate initial states the intra-chain asymmetry dominates, producing KPZ scaling even when the hopping rate is negative. This is presented as a counterexample motivating a theory of charge transport in open systems beyond the SSB ansatz.

Significance. If the equivalence mapping and the dominance of KPZ scaling hold, the result is significant: it supplies a concrete, integrable open-system example in which the SSB ansatz fails to capture the emergent hydrodynamics and nontrivial KPZ behavior appears. The identification of initial-state conditions under which intra-chain asymmetry overrides inter-chain effects supplies a falsifiable criterion that can guide further analytic and numerical work on open-system transport.

major comments (2)
  1. [Model equivalence / mapping section] The equivalence of the B3 model to two interacting asymmetric XXZ spin chains is the load-bearing technical step. The explicit operator mapping, the origin of the intra-chain asymmetry, and the reduction of the Lindblad dynamics to the claimed XXZ form must be derived in full (including any approximations) so that the statement that the SSB ansatz “can only capture the influence of the inter-chain interactions” can be verified independently.
  2. [Dynamics and initial-state section] The claim that the asymmetric XXZ structure dominates the dynamics for suitable initial states (including negative hopping) and produces KPZ scaling is central. Concrete evidence—either an analytic argument for the scaling exponent or numerical data with error bars showing the KPZ roughness and growth exponents—must be supplied; the abstract states the result without derivation details or error analysis.
minor comments (2)
  1. The abstract and introduction should state the precise Lindblad operators defining the B3 model and cite the original reference in which it was introduced.
  2. Notation for the two chains and the inter- versus intra-chain couplings should be introduced once and used consistently throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. The comments highlight areas where additional technical detail will strengthen the manuscript. We address each major comment below and will incorporate the requested material in a revised version.

read point-by-point responses

  1. Referee: [Model equivalence / mapping section] The equivalence of the B3 model to two interacting asymmetric XXZ spin chains is the load-bearing technical step. The explicit operator mapping, the origin of the intra-chain asymmetry, and the reduction of the Lindblad dynamics to the claimed XXZ form must be derived in full (including any approximations) so that the statement that the SSB ansatz “can only capture the influence of the inter-chain interactions” can be verified independently.

    Authors: We agree that the mapping is the central technical foundation and that its current presentation requires expansion for independent verification. In the revised manuscript we will add a dedicated subsection deriving the explicit operator mapping from the B3 Lindblad operators to the two-chain asymmetric XXZ Hamiltonian plus inter-chain terms. The derivation will start from the original jump operators, identify the intra-chain asymmetry terms that arise directly from the B3 structure, and show the reduction of the master equation to the claimed form without further approximations. This will make explicit that the SSB ansatz accounts only for the inter-chain coupling. revision: yes

  2. Referee: [Dynamics and initial-state section] The claim that the asymmetric XXZ structure dominates the dynamics for suitable initial states (including negative hopping) and produces KPZ scaling is central. Concrete evidence—either an analytic argument for the scaling exponent or numerical data with error bars showing the KPZ roughness and growth exponents—must be supplied; the abstract states the result without derivation details or error analysis.

    Authors: We accept that the abstract and main text would benefit from more explicit supporting evidence. The manuscript already contains numerical time-evolution data for selected initial states that exhibit the KPZ roughness and growth exponents, including cases with negative hopping. In the revision we will add a new subsection presenting these data with statistical error bars obtained from multiple independent runs, together with a brief analytic argument showing that, for initial states in which inter-chain correlations remain small, the intra-chain asymmetric XXZ terms dominate the long-wavelength dynamics and enforce KPZ scaling. Additional simulations for negative hopping rates will be included to confirm persistence of the scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents the B3 model equivalence to two interacting asymmetric XXZ spin chains as a derived mapping independent of the SSB ansatz, with the ansatz only capturing inter-chain effects while intra-chain asymmetry produces KPZ for suitable states. No step reduces a claimed prediction or first-principles result to a fitted input, self-citation chain, or definitional equivalence by construction. The central claims rest on explicit model rewriting and initial-state dependence rather than renaming or smuggling via prior self-work. This is the common case of a self-contained derivation against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard definition of the B3 model and its mapping to XXZ chains, which are treated as given from prior integrable-system literature; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The B3 model admits an exact mapping to two interacting asymmetric XXZ spin chains.
    Invoked to explain why the SSB ansatz captures only inter-chain effects while asymmetric structure can dominate.
  • domain assumption Standard open-system dynamics (master equation) govern the evolution.
    Implicit in any discussion of open integrable systems and charge transport.

pith-pipeline@v0.9.1-grok · 5716 in / 1323 out tokens · 45932 ms · 2026-07-03T11:48:34.029868+00:00 · methodology

0 comments
read the original abstract

The universality of dynamical scaling laws constitutes a cornerstone in the theoretical understanding of quantum many-body systems, particularly in non-equilibrium settings. Recent advancements have proposed a phenomenological ansatz based on spontaneous symmetry breaking (SSB) to unify the description of charge transport in open quantum systems. However, it remains unclear under which conditions it fails to capture the emergent hydrodynamics and if it does break down, whether nontrivial dynamics emerge. In this work we show that Kardar-Parisi-Zhang (KPZ) dynamics in an open integrable model (the B3 model), rather than diffusion from SSB, emerges. We find that the B3 model is equivalent to two interacting asymmetric XXZ spin chains and the ansatz can only capture the influence of the inter-chain interactions. When the initial state is appropriate, the asymmetric XXZ structure dominates the dynamics, which gives KPZ scaling behavior even when the hopping rate becomes negative. Our work motivates theory of charge transport in open systems beyond the ansatz based on SSB.

Figures

Figures reproduced from arXiv: 2607.02341 by and Xu-Bo Zou, Chang-Ling Zou, Guang-Can Guo, Guo-Qiang Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · 2 internal anchors

  1. [1]

    Effective field theory of dissipative fluids,

    M. Crossley, P. Glorioso, and H. Liu, “Effective field theory of dissipative fluids,” JHEP09, 095 (2017)

    work page 2017

  2. [2]

    Correc- tions to diffusion in interacting quantum systems,

    A. A. Michailidis, D. A. Abanin, and L. V . Delacr´etaz, “Correc- tions to diffusion in interacting quantum systems,” Phys. Rev. X 14, 031020 (2024)

    work page 2024

  3. [3]

    Full counting statistics of charge in chaotic many- body quantum systems,

    E. McCulloch, J. De Nardis, S. Gopalakrishnan, and R. Vasseur, “Full counting statistics of charge in chaotic many- body quantum systems,” Phys. Rev. Lett.131, 210402 (2023)

    work page 2023

  4. [4]

    Anomalous diffusion in dipole- and higher-moment- conserving systems,

    J. Feldmeier, P. Sala, G. De Tomasi, F. Pollmann, and M. Knap, “Anomalous diffusion in dipole- and higher-moment- conserving systems,” Phys. Rev. Lett.125, 245303 (2020)

    work page 2020

  5. [5]

    Fracton superfluid hydrodynamics,

    C. Stahl, M. Qi, P. Glorioso, A. Lucas, and R. Nandkishore, “Fracton superfluid hydrodynamics,” Phys. Rev. B108, 144509 (2023)

    work page 2023

  6. [6]

    Subdiffusion in strongly tilted lattice systems,

    P. Zhang, “Subdiffusion in strongly tilted lattice systems,” Phys. Rev. Res.2, 033129 (2020)

    work page 2020

  7. [7]

    Kinetically constrained freezing transition in a dipole-conserving system,

    A. Morningstar, V . Khemani, and D. A. Huse, “Kinetically constrained freezing transition in a dipole-conserving system,” Phys. Rev. B101, 214205 (2020)

    work page 2020

  8. [8]

    Kardar-parisi- zhang physics in the quantum heisenberg magnet,

    M. Ljubotina, M. ˇZnidariˇc, and T. Prosen, “Kardar-parisi- zhang physics in the quantum heisenberg magnet,” Phys. Rev. Lett.122, 210602 (2019)

    work page 2019

  9. [9]

    Superuniversality of superdiffusion,

    E. Ilievski, J. De Nardis, S. Gopalakrishnan, R. Vasseur, and B. Ware, “Superuniversality of superdiffusion,” Phys. Rev. X 11, 031023 (2021)

    work page 2021

  10. [10]

    Kinetic theory of spin dif- fusion and superdiffusion inxxzspin chains,

    S. Gopalakrishnan and R. Vasseur, “Kinetic theory of spin dif- fusion and superdiffusion inxxzspin chains,” Phys. Rev. Lett. 122, 127202 (2019)

    work page 2019

  11. [11]

    Dynamics of magnetization at infinite tem- perature in a heisenberg spin chain,

    E. Rosenberget al., “Dynamics of magnetization at infinite tem- perature in a heisenberg spin chain,” Science384, 48 (2024)

    work page 2024

  12. [12]

    Quantum gas microscopy of kardar- parisi-zhang superdiffusion,

    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, “Quantum gas microscopy of kardar- parisi-zhang superdiffusion,” Science376, 716 (2022)

    work page 2022

  13. [13]

    Rigorous bound on hy- drodynamic diffusion for chaotic open spin chains,

    D. Ampelogiannis and B. Doyon, “Rigorous bound on hy- drodynamic diffusion for chaotic open spin chains,” arXiv: 2501.07749 (2025)

    work page arXiv 2025

  14. [14]

    Semiclassical theory of quantum stochastic resistors,

    T. Jin, J. a. Ferreira, M. Bauer, M. Filippone, and T. Giamarchi, “Semiclassical theory of quantum stochastic resistors,” Phys. Rev. Res.5, 013033 (2023)

    work page 2023

  15. [15]

    From stochastic spin chains to quantum kardar-parisi-zhang dynamics,

    T. Jin, A. Krajenbrink, and D. Bernard, “From stochastic spin chains to quantum kardar-parisi-zhang dynamics,” Phys. Rev. Lett.125, 040603 (2020)

    work page 2020

  16. [16]

    Transport and nonreciprocity in monitored quantum devices: An exact study,

    J. a. Ferreira, T. Jin, J. Mannhart, T. Giamarchi, and M. Fil- ippone, “Transport and nonreciprocity in monitored quantum devices: An exact study,” Phys. Rev. Lett.132, 136301 (2024)

    work page 2024

  17. [17]

    Unified interface model for dissipative transport of bosons and fermions,

    Y . Minoguchi, J. Huber, L. Garbe, A. Gambassi, and P. Rabl, “Unified interface model for dissipative transport of bosons and fermions,” Phys. Rev. Lett.134, 207102 (2025)

    work page 2025

  18. [18]

    Superdiffusive transport in quasi-particle dephasing models,

    Y .-P. Wang, C. Fang, and J. Ren, “Superdiffusive transport in quasi-particle dephasing models,” SciPost Phys.17, 150 (2024)

    work page 2024

  19. [19]

    Transport in open quantum systems in the presence of lossy channels,

    K. Ganguly, M. Kulkarni, and B. K. Agarwalla, “Transport in open quantum systems in the presence of lossy channels,” Phys. Rev. B110, 235425 (2024)

    work page 2024

  20. [20]

    Unifying emergent hydrodynamics and lindbladian low-energy spectra across sym- metries, constraints, and long-range interactions,

    O. Ogunnaike, J. Feldmeier, and J. Y . Lee, “Unifying emergent hydrodynamics and lindbladian low-energy spectra across sym- metries, constraints, and long-range interactions,” Phys. Rev. Lett.131, 220403 (2023)

    work page 2023

  21. [21]

    Spontaneous symmetry breaking and nambu-goldstone modes in open classical and quantum sys- tems,

    Y . Hidaka and Y . Minami, “Spontaneous symmetry breaking and nambu-goldstone modes in open classical and quantum sys- tems,” Progress of Theoretical and Experimental Physics2020, 033A01 (2020)

    work page 2020

  22. [22]

    On the Generators of Quantum Dynamical Semi- groups,

    G. Lindblad, “On the Generators of Quantum Dynamical Semi- groups,” Commun. Math. Phys.48, 119 (1976)

    work page 1976

  23. [23]

    Atomic theory of theλtransition in helium,

    R. P. Feynman, “Atomic theory of theλtransition in helium,” Phys. Rev.91, 1291 (1953)

    work page 1953

  24. [24]

    Atomic theory of the two-fluid model of liquid helium,

    R. P. Feynman, “Atomic theory of the two-fluid model of liquid helium,” Phys. Rev.94, 262 (1954)

    work page 1954

  25. [25]

    Magneto-roton theory of collective excitations in the fractional quantum hall effect,

    S. M. Girvin, A. H. MacDonald, and P. M. Platzman, 6 “Magneto-roton theory of collective excitations in the fractional quantum hall effect,” Phys. Rev. B33, 2481 (1986)

    work page 1986

  26. [26]

    Observing emergent hy- drodynamics in a long-range quantum magnet,

    M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, “Observing emergent hy- drodynamics in a long-range quantum magnet,” Science376, 720 (2022)

    work page 2022

  27. [27]

    Nonlocal emergent hy- drodynamics in a long-range quantum spin system,

    A. Schuckert, I. Lovas, and M. Knap, “Nonlocal emergent hy- drodynamics in a long-range quantum spin system,” Phys. Rev. B101, 020416(R) (2020)

    work page 2020

  28. [28]

    Constructing inte- grable lindblad superoperators,

    M. de Leeuw, C. Paletta, and B. Pozsgay, “Constructing inte- grable lindblad superoperators,” Phys. Rev. Lett.126, 240403 (2021)

    work page 2021

  29. [29]

    Integrable nonunitary quantum circuits,

    L. Su and I. Martin, “Integrable nonunitary quantum circuits,” Phys. Rev. B106, 134312 (2022)

    work page 2022

  30. [30]

    Yang-baxter integrable open quantum systems,

    C. Paletta, “Yang-baxter integrable open quantum systems,” arXiv: 2312.00064 (2023)

    work page arXiv 2023

  31. [31]

    Dynamic scaling of growing interfaces,

    M. Kardar, G. Parisi, and Y .-C. Zhang, “Dynamic scaling of growing interfaces,” Phys. Rev. Lett.56, 889 (1986)

    work page 1986

  32. [32]

    Bethe ansatz solution for crossover scaling functions of the asymmetric xxz chain and the kardar-parisi-zhang-type growth model,

    D. Kim, “Bethe ansatz solution for crossover scaling functions of the asymmetric xxz chain and the kardar-parisi-zhang-type growth model,” Phys. Rev. E52, 3512 (1995)

    work page 1995

  33. [33]

    Bethe solution for the dynamical- scaling exponent of the noisy burgers equation,

    L.-H. Gwa and H. Spohn, “Bethe solution for the dynamical- scaling exponent of the noisy burgers equation,” Phys. Rev. A 46, 844 (1992)

    work page 1992

  34. [34]

    Time-reversal invariance and universality of two-dimensional growth models,

    M. Plischke, Z. R ´acz, and D. Liu, “Time-reversal invariance and universality of two-dimensional growth models,” Phys. Rev. B35, 3485 (1987)

    work page 1987

  35. [35]

    Completely positive linear maps on complex ma- trices,

    M.-D. Choi, “Completely positive linear maps on complex ma- trices,” Linear Algebra and its Applications10, 285 (1975)

    work page 1975

  36. [36]

    Here we just choosex=− γ 2 q γ 2 comparing with the original model

    Lindblad master equation is invariant under transformation (h,l)→(h+i(xl † −x ∗l),l+2x)for any complex numberx. Here we just choosex=− γ 2 q γ 2 comparing with the original model

    work page

  37. [37]

    Spontaneous symmetry break- ing in open quantum systems: Strong, weak, and strong-to- weak,

    D. Gu, Z. Wang, and Z. Wang, “Spontaneous symmetry break- ing in open quantum systems: Strong, weak, and strong-to- weak,” Physical Review B112(2025), 10.1103/3g6d-gn7b

    work page doi:10.1103/3g6d-gn7b 2025

  38. [38]

    Supplementary material for derivations

    “Supplementary material for derivations.”

    work page

  39. [39]

    The bethe ansatz for a new inte- grable open quantum system,

    M. de Leeuw and C. Paletta, “The bethe ansatz for a new inte- grable open quantum system,” arXiv: 2207.14193 (2022)

    work page arXiv 2022

  40. [40]

    Efficient simulation of one-dimensional quantum many-body systems,

    G. Vidal, “Efficient simulation of one-dimensional quantum many-body systems,” Phys. Rev. Lett.93, 040502 (2004)

    work page 2004

  41. [41]

    Simulation meth- ods for open quantum many-body systems,

    H. Weimer, A. Kshetrimayum, and R. Or ´us, “Simulation meth- ods for open quantum many-body systems,” Rev. Mod. Phys. 93, 015008 (2021)

    work page 2021

  42. [42]

    Exact scaling functions for one-dimensional stationary kpz growth,

    M. Pr ¨ahofer and H. Spohn, “Exact scaling functions for one-dimensional stationary kpz growth,” Journal of Statistical Physics115, 255 (2004)

    work page 2004

  43. [43]

    Exact scaling functions for one-dimensional stationary kpz growth,

    M. Pr ¨ahofer, “Exact scaling functions for one-dimensional stationary kpz growth,”https://collab.dvb.bayern/ spaces/~gi23qul/pages/56921798/Exact+scaling+ functions+for+one-dimensional+stationary+KPZ+ growth

    work page arXiv

  44. [44]

    Relaxation times of dissipative many-body quan- tum systems,

    M. ˇZnidariˇc, “Relaxation times of dissipative many-body quan- tum systems,” Phys. Rev. E92, 042143 (2015)

    work page 2015

  45. [45]

    The extra factor(1+γ 2)is from the fact that our B3 model transform to the B3 model in [39] via(h,l)→((1+ γ2)−1h,(1+γ 2)−1/2l)

    work page

  46. [46]

    A Rydberg quantum simulator,

    H. Weimer, M. M ¨uller, I. Lesanovsky, P. Zoller, and H. P. B¨uchler, “A Rydberg quantum simulator,” Nature Physics6, 382 (2010)

    work page 2010

  47. [47]

    Many-body physics with indi- vidually controlled Rydberg atoms,

    A. Browaeys and T. Lahaye, “Many-body physics with indi- vidually controlled Rydberg atoms,” Nature Physics16, 132 (2020)

    work page 2020

  48. [48]

    V olcano architecture for scalable quantum processor units,

    D.-Q. Ma, Q.-X. Jie, Y .-D. Hu, W.-Y . Zhu, Y .-C. Zhang, H.- J. Fan, X.-K. Zhong, G.-J. Chen, Y .-L. Zhang, T.-Y . Zhang, X.-F. Ren, L. Chen, Z.-B. Wang, G.-C. Guo, and C.-L. Zou, “V olcano architecture for scalable quantum processor units,” Science China Physics, Mechanics & Astronomy69, 220314 (2026)

    work page 2026

  49. [49]

    Classical representation of the dynamics of quantum spin chains

    T. Jin, “Classical representation of the dynamics of quantum spin chains,” arXiv: 2502.10502 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  50. [50]

    Quantum-to-Classical Computability Transition via Negative Markov Chains

    H. L ´oio, J. D. Nardis, and T. Jin, “Quantum-to-classical computability transition via negative markov chains,” arXiv: 2604.19889 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  51. [51]

    Markov process representation of semigroups whose generators include negative rates,

    F. V ¨ollering, “Markov process representation of semigroups whose generators include negative rates,” arXiv: 2002.01805 (2020)

    work page arXiv 2002