pith. sign in

arxiv: 2408.08249 · v1 · submitted 2024-08-15 · ❄️ cond-mat.str-el · cond-mat.mes-hall· cond-mat.quant-gas· cond-mat.stat-mech· quant-ph

Probing hydrodynamic crossovers with dissipation-assisted operator evolution

N. S. Srivatsa , Oliver Lunt , Tibor Rakovszky , Curt von Keyserlingk This is my paper

Pith reviewed 2026-05-23 22:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallcond-mat.quant-gascond-mat.stat-mechquant-ph
keywords diffusionhydrodynamicscharge densityoperator evolutionlattice modeltransport crossoverconserved densitiescorrelation functions
0
0 comments X

The pith

Diffusion constant scales as D proportional to one over rho at low charge densities in lattice models.

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

The paper uses artificial dissipation to control entanglement growth and track how transport crosses from ballistic to diffusive in an interacting lattice model with conserved U(1) charge at different densities. A generalized version of the dissipation-assisted operator evolution algorithm approximates non-local operators by their ensemble averages instead of discarding them, which keeps operator entanglement manageable while still producing reliable diffusion constants at all densities. The work reports that the diffusion constant falls proportionally to one over density when density is low. A minimal model of the crossover is introduced whose predicted charge correlation functions match the numerical results. These findings identify the leading terms in hydrodynamic correlation functions for conserved densities.

Core claim

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as D ∝ 1/ρ at low densities ρ. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate

What carries the argument

Generalized Dissipation-Assisted Operator Evolution algorithm that approximates non-local operators by ensemble averages rather than discarding them.

If this is right

  • Diffusion constant scales as D ∝ 1/ρ at low densities ρ.
  • Minimal model for the transport crossover produces charge correlation functions that agree with numerical data.
  • Artificial dissipation reduces operator entanglement entropy while preserving accurate diffusion constants at all densities.
  • Results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities.

Where Pith is reading between the lines

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

  • The approximation of non-local operators could be tested in models with additional conserved quantities such as energy or momentum.
  • The observed scaling may guide analytic predictions for dilute limits in other lattice systems.
  • Similar dissipation-assisted methods might be applied to finite-temperature regimes where scattering lengths are harder to access.
  • The minimal model could be extended to predict higher-order correlation functions beyond the charge sector.

Load-bearing premise

Approximating non-local operators by their ensemble averages still produces accurate diffusion constants across all density scales without introducing uncontrolled errors from the artificial dissipation.

What would settle it

Exact or dissipation-free calculations that find the diffusion constant does not scale as 1 over rho at low densities, or that the minimal model fails to match the correlation functions, would disprove the central claims.

Figures

Figures reproduced from arXiv: 2408.08249 by Curt von Keyserlingk, N. S. Srivatsa, Oliver Lunt, Tibor Rakovszky.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the spin diffusion constant [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

Using artificial dissipation to tame entanglement growth, we chart the emergence of diffusion in a generic interacting lattice model for varying U(1) charge densities. We follow the crossover from ballistic to diffusive transport above a scale set by the scattering length, finding the intuitive result that the diffusion constant scales as $D \propto 1/\rho$ at low densities $\rho$. Our numerical approach generalizes the Dissipation-Assisted Operator Evolution (DAOE) algorithm: in the spirit of the BBGKY hierarchy, we effectively approximate non-local operators by their ensemble averages, rather than discarding them entirely. This greatly reduces the operator entanglement entropy, while still giving accurate predictions for diffusion constants across all density scales. We further construct a minimal model for the transport crossover, yielding charge correlation functions which agree well with our numerical data. Our results clarify the dominant contributions to hydrodynamic correlation functions of conserved densities, and serve as a guide for generalizations to low temperature transport.

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

0 major / 2 minor

Summary. The paper generalizes the Dissipation-Assisted Operator Evolution (DAOE) method by approximating non-local operators via ensemble averages (in the spirit of the BBGKY hierarchy) to study the ballistic-to-diffusive crossover in a generic U(1)-conserving lattice model at varying charge densities ρ. It reports that the diffusion constant scales as D ∝ 1/ρ at low ρ, supplies explicit comparisons to exact small-system data, and constructs a parameter-free minimal model whose charge correlation functions match the numerical results across densities.

Significance. If the central claims hold, the work supplies a controlled numerical route to hydrodynamic correlation functions of conserved densities and demonstrates that the ensemble-average approximation reduces operator entanglement while remaining accurate for diffusion constants at all densities. The parameter-free minimal model and its agreement with numerics constitute a clear strength, as does the explicit density scaling result.

minor comments (2)
  1. The definition of the scattering length and its relation to the crossover scale should be stated explicitly in the main text (currently only referenced in the abstract).
  2. Figure captions for the correlation-function comparisons should include the system sizes and dissipation strengths used, to allow direct assessment of finite-size effects.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work and for recommending acceptance of the manuscript. We are pleased that the generalization of DAOE via ensemble averages, the D ∝ 1/ρ scaling, and the agreement of the parameter-free minimal model with numerics were viewed as strengths.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation relies on a generalized DAOE procedure that approximates non-local operators via ensemble averages (reducing entanglement while matching diffusion constants across densities) and a parameter-free minimal model whose correlation functions are compared to independent numerical data and exact small-system benchmarks. No load-bearing step reduces by construction to a fitted input, self-definition, or self-citation chain; the central claims (D ∝ 1/ρ scaling and crossover agreement) remain independently falsifiable against the reported numerics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central numerical claims rest on the validity of replacing non-local operators by ensemble averages and on the assumption that added dissipation does not alter the hydrodynamic scaling.

axioms (1)
  • domain assumption Approximating non-local operators by their ensemble averages yields accurate predictions for diffusion constants across density scales.
    This is the key modification to DAOE described in the abstract.

pith-pipeline@v0.9.0 · 5721 in / 1246 out tokens · 24442 ms · 2026-05-23T22:24:59.877535+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 1 Pith paper

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

  1. Reweighted Time-Evolving Block Decimation for Improved Quantum Dynamics Simulations

    quant-ph 2024-12 unverdicted novelty 7.0

    rTEBD reweights truncation in TEBD for MPDOs by a factor γ^{-n} on weight-n terms, producing higher accuracy than standard MPDO TEBD, competitive or superior results to MPS TEBD, and improved preservation of conserved...

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · cited by 1 Pith paper

  1. [1]

    Forster,Hydrodynamic Fluctuations, Broken Symme- try, and Correlation Functions(CRC Press, Boca Raton, 2019)

    D. Forster,Hydrodynamic Fluctuations, Broken Symme- try, and Correlation Functions(CRC Press, Boca Raton, 2019)

    work page 2019

  2. [2]

    Physics at the Fundamental Frontier

    H. Liu and P. Glorioso, Lectures on non-equilibrium ef- fective field theories and fluctuating hydrodynamics, in Proceedings of Theoretical Advanced Study Institute Sum- mer School 2017 “Physics at the Fundamental Frontier” (TASI2017), Vol. 305 (SISSA Medialab, 2018) p. 008

    work page 2017

  3. [3]

    Mukerjee, V

    S. Mukerjee, V. Oganesyan, and D. Huse, Statistical the- ory of transport by strongly interacting lattice fermions, Physical Review B73, 035113 (2006)

    work page 2006

  4. [4]

    Gopalakrishnan and R

    S. Gopalakrishnan and R. Vasseur, Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains, Physical Review Letters122, 127202 (2019)

    work page 2019

  5. [5]

    De Nardis, D

    J. De Nardis, D. Bernard, and B. Doyon, Diffusion in generalized hydrodynamics and quasiparticle scattering, SciPost Physics6, 049 (2019)

    work page 2019

  6. [6]

    Karrasch, D

    C. Karrasch, D. M. Kennes, and J. E. Moore, Transport properties of the one-dimensional Hubbard model at finite temperature, Physical Review B90, 155104 (2014)

    work page 2014

  7. [7]

    Rakovszky, C

    T. Rakovszky, C. W. von Keyserlingk, and F. Pollmann, Dissipation-assisted operator evolution method for cap- turing hydrodynamic transport, Physical Review B105, 075131 (2022)

    work page 2022

  8. [8]

    von Keyserlingk, F

    C. von Keyserlingk, F. Pollmann, and T. Rakovszky, Op- erator backflow and the classical simulation of quantum transport, Physical Review B105, 245101 (2022)

    work page 2022

  9. [9]

    Lloyd, T

    J. Lloyd, T. Rakovszky, F. Pollmann, and C. von Key- serlingk, The ballistic to diffusive crossover in a weakly- interacting Fermi gas (2023), arxiv:2310.16043

    work page arXiv 2023

  10. [10]

    E.-J. Kuo, B. Ware, P. Lunts, M. Hafezi, and C. D. White, Energy diffusion in weakly interacting chains with fermionic dissipation-assisted operator evolution (2023), arXiv:2311.17148

    work page arXiv 2023

  11. [11]

    N. N. Bogolyubov,Lectures on Quantum Statistics(CRC Press, 1970)

    work page 1970

  12. [12]

    Kardar,Statistical Physics of Particles(Cambridge University Press, 2007)

    M. Kardar,Statistical Physics of Particles(Cambridge University Press, 2007)

    work page 2007

  13. [13]

    C. D. White, M. Zaletel, R. S. K. Mong, and G. Refael, Quantum dynamics of thermalizing systems, Physical Review B97, 035127 (2018)

    work page 2018

  14. [14]

    Klein Kvorning, L

    T. Klein Kvorning, L. Herviou, and J. H. Bardarson, Time- evolution of local information: Thermalization dynamics of local observables, SciPost Physics13, 080 (2022)

    work page 2022

  15. [15]

    Artiaco, C

    C. Artiaco, C. Fleckenstein, D. Aceituno Chávez, T. K. Kvorning, and J. H. Bardarson, Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution, PRX Quantum5, 020352 (2024)

    work page 2024

  16. [16]

    S. N. Thomas, B. Ware, J. D. Sau, and C. D. White, Comparing numerical methods for hydrodynamics in a 1D lattice model (2023), arxiv:2310.06886

    work page arXiv 2023

  17. [17]

    Frías-Pérez, L

    M. Frías-Pérez, L. Tagliacozzo, and M. C. Bañuls, Con- verting Long-Range Entanglement into Mixture: Tensor- Network Approach to Local Equilibration, Physical Re- 6 view Letters132, 100402 (2024)

    work page 2024

  18. [18]

    D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, A Universal Operator Growth Hypothesis, Physical Review X9, 041017 (2019)

    work page 2019

  19. [19]

    Nahum, S

    A. Nahum, S. Vijay, and J. Haah, Operator Spreading in Random Unitary Circuits, Physical Review X8, 021014 (2018)

    work page 2018

  20. [20]

    Khemani, A

    V. Khemani, A. Vishwanath, and D. A. Huse, Operator Spreading and the Emergence of Dissipative Hydrody- namics under Unitary Evolution with Conservation Laws, Physical Review X8, 031057 (2018)

    work page 2018

  21. [21]

    C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws, Physical Review X8, 021013 (2018)

    work page 2018

  22. [22]

    Rakovszky, F

    T. Rakovszky, F. Pollmann, and C. W. von Keyserlingk, Diffusive Hydrodynamics of Out-of-Time-Ordered Corre- lators with Charge Conservation, Physical Review X8, 031058 (2018)

    work page 2018

  23. [23]

    Steinigeweg, F

    R. Steinigeweg, F. Heidrich-Meisner, J. Gemmer, K. Michielsen, and H. De Raedt, Scaling of diffusion constants in the spin-1 2 XX ladder, Physical Review B90, 094417 (2014)

    work page 2014

  24. [24]

    Karrasch, D

    C. Karrasch, D. M. Kennes, and F. Heidrich-Meisner, Spin and thermal conductivity of quantum spin chains and ladders, Physical Review B91, 115130 (2015)

    work page 2015

  25. [25]

    Kloss, Y

    B. Kloss, Y. B. Lev, and D. Reichman, Time-dependent variational principle in matrix-product state manifolds: Pitfalls and potential, Physical Review B 97, 024307 (2018)

    work page 2018

  26. [26]

    Žnidarič, Coexistence of Diffusive and Ballistic Trans- port in a Simple Spin Ladder, Physical Review Letters 110, 070602 (2013)

    M. Žnidarič, Coexistence of Diffusive and Ballistic Trans- port in a Simple Spin Ladder, Physical Review Letters 110, 070602 (2013)

    work page 2013

  27. [27]

    Sachdev,Quantum Phase Transitions, 2nd ed

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

    work page 2011

  28. [28]

    1 Supplemental Material for ‘Probing hydrodynamic crossovers with dissipation-assisted operator evolution’ S1

    See the Supplemental Material for details of the mem- ory matrix calculation for charge correlation functions; a discussion of the operator weight distribution after per- forming DAOEµ; supporting evidence for our argument about the failure of DAOE0 at low fillings; and analysis of the convergence of diffusion constants with the dissipation strength. 1 Su...

    work page