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arxiv: 2604.23192 · v1 · submitted 2026-04-25 · 🪐 quant-ph · cond-mat.stat-mech

Recognition: unknown

Coherence dynamics in quantum many-body systems with conservation laws

Sreemayee Aditya , Emanuele Tirrito , Piotr Sierant , Xhek Turkeshi
Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:29 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords coherence dynamicsconservation lawsquantum many-body systemshydrodynamic relaxationU(1) symmetryrandom circuitsthermalization
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The pith

Conservation laws in quantum many-body systems replace logarithmic saturation of coherence with slow hydrodynamic relaxation.

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

The paper examines how conservation laws influence the spreading of quantum coherence in many-body systems. Focusing on symmetric random circuits and ergodic Hamiltonians, it shows that these laws change the behavior of coherence. Instead of quick logarithmic saturation, global coherence relaxes slowly through hydrodynamic processes. Locally, constrained systems display a rise to a peak followed by a fall, with the peak time increasing algebraically as the subsystem size grows. Ergodic dynamics create longer plateaus instead.

Core claim

The central claim is that conservation laws shape coherence spreading in quantum many-body dynamics by substituting the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of global coherence measures such as the participation entropy. Locally, the relative entropy of coherence in symmetry-constrained circuits exhibits a rise-peak-fall structure, with the peak time growing algebraically with subsystem size. Ergodic Hamiltonian dynamics, however, broaden this peak into an extended plateau for larger subsystems. This establishes coherence as a sensitive probe of symmetry-constrained thermalization and its relation to many-body transport.

What carries the argument

Hydrodynamic relaxation of coherence measures due to conservation laws in U(1)-symmetric and dipole-conserving circuits and Hamiltonians, measured globally by participation entropy and locally by relative entropy of coherence.

If this is right

  • Global coherence measures undergo slow hydrodynamic relaxation.
  • Local coherence in symmetry-constrained circuits shows a rise-peak-fall with algebraic scaling of peak time.
  • Ergodic cases show broadened plateaus in local coherence.
  • Coherence acts as a probe linking resource dynamics to transport.

Where Pith is reading between the lines

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

  • Coherence monitoring might allow experimental access to hydrodynamic transport in quantum simulators without measuring currents directly.
  • The algebraic scaling could be tested in larger systems to confirm universality beyond the studied models.
  • Similar patterns may emerge in systems with other symmetries, extending the connection to general constrained dynamics.

Load-bearing premise

That the U(1)-symmetric random circuits, charge-and-dipole conserving circuits, and ergodic Hamiltonians studied here, along with the combination of exact, MPS, and replica tensor network methods, capture the universal long-time coherence behavior without significant model-specific or finite-size artifacts.

What would settle it

Finding logarithmic saturation of global coherence measures persisting at long times in a conserved-charge system, or observing that the peak time of local coherence does not increase with subsystem size in constrained circuits, would disprove the main results.

Figures

Figures reproduced from arXiv: 2604.23192 by Emanuele Tirrito, Piotr Sierant, Sreemayee Aditya, Xhek Turkeshi.

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read the original abstract

We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences both globally, via the participation entropy, and locally, via the relative entropy of coherence. Combining exact vector evolution, matrix product state simulations, and replica tensor networks methods, we find that conservation laws replace the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of the global coherence measures. Locally, symmetry-constrained circuits show a clean rise-peak-fall structure whose peak time grows algebraically with subsystem size. In contrast, ergodic Hamiltonians broaden the peak into an extended plateau at larger subsystems, highlighting a qualitatively distinct mechanism. Coherence thus emerges as a sensitive probe of symmetry-constrained thermalization, linking quantum resource dynamics to many-body 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

2 major / 1 minor

Summary. The manuscript examines the influence of conservation laws on the spreading of quantum coherence in many-body systems. It focuses on U(1)-symmetric random circuits, charge-and-dipole conserving circuits, and ergodic Hamiltonian dynamics. Using exact vector evolution, matrix product state simulations, and replica tensor networks, the authors report that conservation laws lead to slow hydrodynamic relaxation of global coherence measures (participation entropy) instead of the logarithmic saturation seen in unconstrained circuits. Locally, symmetry-constrained circuits exhibit a rise-peak-fall structure in the relative entropy of coherence, with the peak time scaling algebraically with subsystem size, while ergodic Hamiltonians show a broadened peak into a plateau at larger subsystems.

Significance. If the reported behaviors are robust against finite-size effects, this work offers a valuable connection between quantum coherence as a resource and many-body transport phenomena under symmetries. The multi-method approach and comparison between circuit and Hamiltonian dynamics are strengths, providing insights into symmetry-constrained thermalization. It could serve as a foundation for further studies on how conservation laws affect quantum information dynamics.

major comments (2)
  1. [Numerical results for local relative entropy of coherence] The central claim of algebraic growth of the local coherence peak time with subsystem size (and the distinction from plateaus in ergodic cases) is load-bearing for the universality argument, yet the manuscript provides no details on the range of subsystem sizes, fitting procedures, or finite-size scaling analysis to confirm the regime is asymptotic rather than contaminated by boundaries or discreteness effects.
  2. [Methods and replica TN implementation] Replica tensor network approximations are used for long-time global and local coherence measures, but without reported error bars, bond-dimension convergence tests, or comparisons to exact evolution at accessible times, it is unclear whether the slow hydrodynamic relaxation is accurately captured or biased by the method's limitations.
minor comments (1)
  1. [Abstract] The abstract would benefit from briefly stating the observed scaling exponent for the peak time or the specific subsystem sizes accessed, to allow immediate assessment of the algebraic claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive major comments. We agree that additional details on finite-size analysis and method validation will strengthen the manuscript. We address each point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Numerical results for local relative entropy of coherence] The central claim of algebraic growth of the local coherence peak time with subsystem size (and the distinction from plateaus in ergodic cases) is load-bearing for the universality argument, yet the manuscript provides no details on the range of subsystem sizes, fitting procedures, or finite-size scaling analysis to confirm the regime is asymptotic rather than contaminated by boundaries or discreteness effects.

    Authors: We agree that explicit documentation of subsystem sizes, fitting procedures, and finite-size scaling is required to substantiate the algebraic scaling claim and its distinction from ergodic plateaus. In the revised manuscript we will add a dedicated subsection (and supplementary figures) reporting the exact range of subsystem sizes examined, the functional forms and fitting windows used to extract the algebraic exponent, and data collapses or scaling plots versus subsystem size that demonstrate the scaling persists beyond boundary or discreteness effects. These additions will directly support the universality argument. revision: yes

  2. Referee: [Methods and replica TN implementation] Replica tensor network approximations are used for long-time global and local coherence measures, but without reported error bars, bond-dimension convergence tests, or comparisons to exact evolution at accessible times, it is unclear whether the slow hydrodynamic relaxation is accurately captured or biased by the method's limitations.

    Authors: We acknowledge that the current presentation lacks quantitative validation of the replica tensor-network results. In the revision we will include (i) error bars derived from replica variance or multiple independent runs, (ii) explicit bond-dimension convergence plots for the global and local observables at representative times, and (iii) direct comparisons between replica TN and exact vector evolution (or MPS) for all system sizes and times where the latter are feasible. These controls will be placed in the Methods section and supplementary material to confirm that the reported hydrodynamic relaxation is not an artifact of the approximation. revision: yes

Circularity Check

0 steps flagged

No circularity: results from explicit numerical simulations of defined models

full rationale

The paper reports numerical observations of coherence dynamics under conservation laws using explicitly defined models (U(1)-symmetric random circuits, charge-and-dipole conserving circuits, ergodic Hamiltonians) evolved via exact diagonalization, MPS, and replica tensor networks. No derivation chain exists that reduces predictions to inputs by construction, no parameters are fitted and relabeled as predictions, and no load-bearing self-citations or ansatzes are invoked to justify core claims. All reported structures (hydrodynamic relaxation, algebraic peak-time scaling, rise-peak-fall vs plateau) are direct outputs of the simulations on finite systems, with no self-definitional loops or renaming of known results as new derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on numerical observations from three classes of models (U(1) random circuits, charge-dipole conserving circuits, ergodic Hamiltonians). No free parameters, axioms, or invented entities are stated in the abstract.

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Forward citations

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  2. Non-Local Magic Resources for Fermionic Gaussian States

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  3. Lecture Notes on Replica Tensor Networks for Random Quantum Circuits

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    Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.

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