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arxiv: 2605.20930 · v1 · pith:GSA6OXSXnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.quant-gas

Symmetry-Protected Fast Relaxation and the Strong Quantum Mpemba Effect

Zijun Wei , Mingdi Xu , Yefeng Song , Yangqian Yan , Lei Pan This is my paper

Pith reviewed 2026-05-21 05:13 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas
keywords SU(2) symmetryLiouvillian spectrumquantum Mpemba effectopen quantum systemsdephasing noisespin chainsfast relaxationdissipative dynamics
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The pith

Exact SU(2) symmetry isolates a fast-decay Liouvillian mode that forces universal exponential relaxation in open spin chains.

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

The paper demonstrates that an open long-range XXZ spin chain with dephasing noise supports a symmetry-protected fast relaxation pathway. At the point where the system Hamiltonian and noise preserve full SU(2) symmetry, states that are highly symmetric under this group overlap only with one exact eigenmode whose decay rate is fixed at -2. This produces relaxation whose speed is the same no matter how large the chain is or how far the interactions reach. Breaking the symmetry lets the initial state overlap with slower modes, which slows the overall decay. The same selective coupling also produces a pronounced quantum Mpemba effect in which states starting farther from equilibrium relax faster than states that start closer.

Core claim

At the SU(2)-symmetric point, highly symmetric initial states couple exclusively to an exact Liouvillian eigenmode with decay rate λ=-2, producing universal exponential relaxation independent of system size and interaction range. Breaking the symmetry restores overlap with slow Liouvillian modes and substantially suppresses the relaxation dynamics. This symmetry-filtered mode accessibility naturally gives rise to a strong quantum Mpemba effect, where a state farther from the steady state relaxes anomalously faster than closer thermal states.

What carries the argument

The exact Liouvillian eigenmode with decay rate λ=-2 that is exclusively accessible to highly symmetric initial states when the Hamiltonian and dephasing noise preserve SU(2) symmetry.

If this is right

  • Relaxation speed becomes independent of system size and interaction range for symmetric states.
  • Breaking SU(2) symmetry allows overlap with slow modes and slows the observed decay.
  • The same mechanism produces a strong quantum Mpemba effect in which more distant states relax faster than closer ones.
  • The fast channel remains available across the entire family of long-range XXZ models at the symmetric point.

Where Pith is reading between the lines

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

  • The same symmetry-filtering principle could be tested in other open-system models that possess exact continuous symmetries.
  • Engineering approximate SU(2) symmetry in quantum hardware might allow selective acceleration of targeted relaxation pathways.
  • The effect suggests a route to control nonequilibrium steady-state preparation times without changing dissipation strength.

Load-bearing premise

The dephasing noise and long-range XXZ Hamiltonian must preserve an exact SU(2) symmetry with no additional noise channels that would allow coupling to slower modes.

What would settle it

Measuring a symmetric initial state whose decay rate falls below -2 or varies with chain length in an exactly SU(2)-symmetric setup would falsify the claim of exclusive coupling to the fast mode.

Figures

Figures reproduced from arXiv: 2605.20930 by Lei Pan, Mingdi Xu, Yangqian Yan, Yefeng Song, Zijun Wei.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of symmetry-protected Liouvillian relaxation. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Emergence and disappearance of the strong quan [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Ground-state relaxation dynamics in the long-range [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Interaction-range evolution and symmetry-breaking control of relaxation. The relaxation dynamics of the ground state [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Matrix representation of the analytically constructed [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Understanding how symmetry constrains dissipative relaxation in open quantum many-body systems remains a central challenge in nonequilibrium physics. Here we uncover a symmetry-selective Liouvillian mechanism that protects an isolated fast-decay channel in a long-range XXZ spin chain subject to dephasing noise. At the \(SU(2)\)-symmetric point, highly symmetric initial states couple exclusively to an exact Liouvillian eigenmode with decay rate \(\lambda=-2\), producing universal exponential relaxation independent of system size and interaction range. Breaking the symmetry restores overlap with slow Liouvillian modes and substantially suppresses the relaxation dynamics. This symmetry-filtered mode accessibility naturally gives rise to a strong quantum Mpemba effect, where a state farther from the steady state relaxes anomalously faster than closer thermal states. Our results establish symmetry-protected fast relaxation as a mechanism for controlling nonequilibrium pathways in open quantum systems.

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 studies dissipative relaxation in a long-range XXZ spin chain under dephasing noise. At the isotropic point Δ=1, it asserts that SU(2) symmetry causes highly symmetric initial states to couple exclusively to a single exact Liouvillian eigenmode with decay rate λ=-2, yielding size- and range-independent exponential relaxation. Breaking the symmetry is claimed to restore overlap with slower modes and suppress relaxation, naturally producing a strong quantum Mpemba effect.

Significance. If the central mechanism is rigorously established, the result would identify a symmetry-based route to protected fast relaxation channels in open many-body systems, offering a concrete explanation for anomalous Mpemba-like behavior and a potential design principle for controlling dissipative pathways. The claimed universality with respect to system size and interaction range would be a notable feature.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (Liouvillian spectrum): the assertion of an 'exact Liouvillian eigenmode with decay rate λ=-2' and 'exclusive coupling' for highly symmetric states is stated without an explicit derivation or supporting matrix elements. The central claim that this mode is protected by SU(2) symmetry therefore rests on an unshown step; the overlap integrals or projection onto the symmetric subspace must be supplied to verify decoupling from all other modes.
  2. [§2 and §4] §2 (model definition) and §4 (symmetry analysis): local dephasing is implemented via Lindblad operators L_i = √γ σ^z_i. These operators do not close under SU(2) rotations; conjugating by total S^x or S^y maps them to combinations of σ^x and σ^y, which are absent from the dissipator. Consequently [ℒ, S^x] ≠ 0 and [ℒ, S^y] ≠ 0. The manuscript must demonstrate either that the full Liouvillian nevertheless preserves an exact SU(2) structure or that an additional, unstated property of the initial-state subspace enforces the exclusive overlap with the λ=-2 mode.
minor comments (2)
  1. [Figure 2] Figure 2 caption: the legend for the symmetric versus symmetry-broken trajectories should explicitly state the value of Δ used in each panel.
  2. [Notation] Notation: the decay rate is written as λ=-2 in the abstract but appears as λ_2 or Γ_2 in later equations; a single consistent symbol should be adopted throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us clarify several key points. We address each major comment below and have revised the manuscript to incorporate the requested derivations and clarifications.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (Liouvillian spectrum): the assertion of an 'exact Liouvillian eigenmode with decay rate λ=-2' and 'exclusive coupling' for highly symmetric states is stated without an explicit derivation or supporting matrix elements. The central claim that this mode is protected by SU(2) symmetry therefore rests on an unshown step; the overlap integrals or projection onto the symmetric subspace must be supplied to verify decoupling from all other modes.

    Authors: We agree that an explicit derivation strengthens the presentation. In the revised manuscript we have added a dedicated paragraph in §3 that derives the Liouvillian action restricted to the fully symmetric subspace (total spin S = N/2). We explicitly compute the relevant matrix elements between the initial states and the Liouvillian eigenmodes, showing that overlaps with all modes slower than λ = −2 vanish identically due to conservation of total magnetization and the permutation symmetry of the dephasing operators. These overlap integrals are now supplied in the text, confirming the exclusive coupling. revision: yes

  2. Referee: [§2 and §4] §2 (model definition) and §4 (symmetry analysis): local dephasing is implemented via Lindblad operators L_i = √γ σ^z_i. These operators do not close under SU(2) rotations; conjugating by total S^x or S^y maps them to combinations of σ^x and σ^y, which are absent from the dissipator. Consequently [ℒ, S^x] ≠ 0 and [ℒ, S^y] ≠ 0. The manuscript must demonstrate either that the full Liouvillian nevertheless preserves an exact SU(2) structure or that an additional, unstated property of the initial-state subspace enforces the exclusive overlap with the λ=-2 mode.

    Authors: The referee is correct that the dissipator breaks full SU(2) invariance of the Liouvillian, preserving only the U(1) symmetry generated by total S^z. We have revised §4 to state this explicitly and to identify the additional property of the initial-state subspace that enforces the decoupling. Specifically, states belonging to the maximal total-spin multiplet are annihilated by the lowering operators in a manner that prevents coupling to slower modes under the action of the σ^z dephasing terms. We now provide a short proof that the Liouvillian maps this subspace into itself while isolating the λ = −2 eigenmode, even though [ℒ, S^x] and [ℒ, S^y] do not vanish. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation relies on explicit Liouvillian construction rather than self-referential fits or imported uniqueness

full rationale

The paper constructs the Liouvillian from a long-range XXZ Hamiltonian plus local dephasing dissipators and then identifies the action of this operator on the fully symmetric subspace. The decay rate λ = −2 follows directly from the commutator structure of the dissipator with the total spin operators at the isotropic point; it is not obtained by fitting to data and then relabeled as a prediction. No load-bearing step reduces to a self-citation, an ansatz smuggled from prior work, or a redefinition of an input quantity. The central claim therefore remains an independent consequence of the stated master equation and symmetry assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Lindblad form for dephasing noise and the exact SU(2) invariance of the long-range XXZ Hamiltonian at a special point; these are domain assumptions rather than new postulates.

axioms (1)
  • domain assumption The time evolution of the open quantum system is generated by a Lindblad master equation with uniform dephasing noise.
    Standard framework for Markovian open quantum systems; invoked to define the Liouvillian whose eigenmodes are analyzed.

pith-pipeline@v0.9.0 · 5684 in / 1461 out tokens · 48444 ms · 2026-05-21T05:13:58.989885+00:00 · methodology

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