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arxiv: 2606.06653 · v1 · pith:HAX5D567new · submitted 2026-06-04 · 🪐 quant-ph · cond-mat.stat-mech

Higher-order Symmetric Quantum Mpemba Effect in Fragmented Systems

Sreemayee Aditya , Sara Murciano , Xhek Turkeshi This is my paper

Pith reviewed 2026-06-28 00:26 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords quantum Mpemba effectHilbert space fragmentationKrylov sectorscharge conservationdipole conservationentanglement asymmetrysymmetry restoration
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The pith

Charge and dipole asymmetries in fragmented systems each exhibit Mpemba-like crossings on parametrically distinct timescales.

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

The paper shows that the quantum Mpemba effect survives in Hilbert spaces fragmented by simultaneous charge and dipole conservation. Greater initial breaking of either symmetry still leads to faster restoration, but the two asymmetries cross on separate timescales. The mechanism is resolved by splitting states into frozen Krylov sectors that keep a fixed asymmetry and active sectors that relax. This turns the original effect into a higher-order version shaped by the conservation laws rather than erased by them.

Core claim

The authors uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.

What carries the argument

The split into frozen and active Krylov sectors set by charge and dipole conservation, which keeps persistent asymmetry in one subset of sectors while allowing relaxation-driven crossings in the other.

If this is right

  • The quantum Mpemba effect persists under strong Hilbert-space fragmentation but appears separately for each conserved moment.
  • Frozen sectors leave a permanent memory of the initial asymmetry while active sectors produce the Mpemba crossing.
  • The same phenomenology appears in both unitary circuits, Hamiltonians, and an exactly solvable dissipative model.
  • Higher-moment symmetries acquire their own Mpemba timescales set by the fragmentation structure.

Where Pith is reading between the lines

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

  • Similar higher-order crossings could appear whenever multiple independent conservation laws fragment the space.
  • The separation of timescales might allow selective control of relaxation for different multipole moments in experiments.
  • Exact solutions in small fragmented systems could be used to test whether the active-sector relaxation rate matches the observed crossing time.

Load-bearing premise

The split between frozen and active Krylov sectors fully explains the observed crossings and that the replica tensor-network and Hamiltonian calculations capture the true long-time dynamics without large finite-size artifacts.

What would settle it

A calculation or simulation in which active sectors are removed or suppressed yet the asymmetry crossings still appear, or one in which the crossings disappear when frozen sectors are eliminated.

Figures

Figures reproduced from arXiv: 2606.06653 by Sara Murciano, Sreemayee Aditya, Xhek Turkeshi.

Figure 1
Figure 1. Figure 1: Schematic and summary of our study. theories [65–68]; whether the higher-order symmetric Mpemba effect persists under energy-conserving evolu￾tion is therefore a question of physical relevance. In this setting circuit averaging is no longer available to re￾cast the dynamics as a replica tensor network. We in￾stead adapt the state-of-the-art Chebyshev polynomial method [69, 70] to the Hamiltonian evolution,… view at source ↗
Figure 2
Figure 2. Figure 2: Von Neumann and R´enyi-2 asymmetries associated with charge and dipole for an initial pure spin-1 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Replica tensor network for the charge- and dipole [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Charge and dipole asymmetry dynamics in a charge- and dipole-conserving Haar-random circuit with [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Frozen and active contributions to the R´enyi-2 entanglement asymmetries for a boundary subsystem in the charge [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Charge and dipole asymmetry dynamics for one-dimensional pair-hopping Hamiltonian of size [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Charge- and dipole R´enyi-2 asymmetries in the symmetric pair-flipping model for subsystems of size [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Self-averaging of the entanglement asymmetry in the charge- and dipole-conserving Haar-random circuit of size [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Charge and dipole asymmetry dynamics in a charge- and dipole-conserving Haar-random circuit with [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Charge and dipole asymmetry dynamics for charge and dipole-conserving circuit of size [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: For the symmetric pair-flipping model at [PITH_FULL_IMAGE:figures/full_fig_p025_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Von-Neumann asymmetries with respect to charge and dipole symmetries in the symmetric pair-flipping model. [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
read the original abstract

A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed R\'enyi-2 entanglement asymmetry up to $L=128$, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.

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 / 3 minor

Summary. The manuscript claims that Hilbert-space fragmentation due to simultaneous charge and dipole conservation does not preclude the quantum Mpemba effect but reshapes it into a higher-order symmetric version: charge and dipole asymmetries each exhibit Mpemba-like crossings on parametrically distinct timescales. This is demonstrated via a replica tensor-network method for the annealed Rényi-2 entanglement asymmetry (reaching L=128), direct Hamiltonian evolution, and an exactly solvable dissipative model. The mechanism is identified by decomposing the state into frozen and active Krylov sectors, where frozen fragments retain finite asymmetry while active fragments drive the relaxation.

Significance. If the results hold, the work supplies a concrete framework for Mpemba phenomenology under higher-moment conservation laws by showing how fragmentation converts the effect into frozen memory plus active-sector relaxation. The combination of three independent lines of evidence—large-scale replica tensor networks, Hamiltonian simulations, and exact solvability—constitutes a clear methodological strength that directly ties the observed crossings to the defining conservation laws without additional dynamical assumptions.

minor comments (3)
  1. [Abstract] Abstract: the claim that the replica tensor-network computation reaches L=128 would be strengthened by a brief statement on convergence checks or error estimates, even if these appear in the main text.
  2. The distinction between frozen and active sectors is derived directly from the charge and dipole conservation laws, but a short explicit statement confirming that the sector decomposition is exhaustive (i.e., no additional sectors are needed) would improve clarity in the mechanism section.
  3. Figure captions for the asymmetry crossings should explicitly label the parametrically distinct timescales for charge versus dipole to make the higher-order character immediately visible.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript, the accurate summary of our results on the higher-order symmetric quantum Mpemba effect, and the recommendation for minor revision. The combination of replica tensor networks, Hamiltonian simulations, and exact solvability is indeed a methodological strength.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper supports its claims via three independent lines of evidence—replica tensor-network computation of annealed Rényi-2 asymmetry (up to L=128), direct Hamiltonian evolution, and an exactly solvable dissipative model—none of which reduce the reported charge/dipole crossings to a fitted parameter or self-defined quantity. The frozen/active Krylov sector decomposition follows directly from the defining charge and dipole conservation laws that generate the fragmentation, without additional dynamical postulates or self-citation chains. No equation equates a prediction to its own input by construction, and the mechanism is a direct consequence of the Hilbert-space structure rather than an ansatz or renamed empirical pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on standard domain assumptions in quantum many-body physics and tensor-network methods; no free parameters or invented entities are explicitly introduced in the provided text.

axioms (2)
  • domain assumption The replica tensor-network formulation reaches the annealed Rényi-2 entanglement asymmetry up to L=128 without uncontrolled approximations.
    Invoked to obtain the numerical evidence for the crossings.
  • domain assumption Krylov sectors can be cleanly partitioned into frozen and active classes whose asymmetry dynamics are independent.
    This partition is used to explain the mechanism behind the observed crossings.

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Forward citations

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Reference graph

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    Total number of fragments LetN frag(L)denotes the total number of Krylov fragments for a chain of lengthLin OBCs. To count Nfrag analytically, we construct a transfer matrix [55–57, 115–117] on the eight three-site configurations {000,001,010,011,100,101,110,111}. The matrix elementT frag(ci, cj)connects the row state(s j, sj+1, sj+2)to the column state(s...

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    Frozen fragments In classically fragmented systems, a basis configuration is frozen if and only if it contains neither 1001 nor 0110 on any contiguous four-site block. The corresponding transfer matrixT fr is constructed in the same way asT frag, but nowbothpatterns are forbidden: Tfr = ⎛ ⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜ ⎝ 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0...

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    sites and a variablexconjugate to the dipole moment, one has D0,0(L)= [xL(L+1)/4 yL/2] L ∏ j=1 (1+x j y),(C8) where[x ayb]f(x, y)denotes the coefficient ofx ayb in the Taylor expansion off. The constrainty L/2 enforcesQ=0 (equal number of+ 1 2 and−1 2 spins), whilex L(L+1)/4 enforcesP=0 (the sum of site indices carryings i =+ 1 2 equals L(L+1)/4). Equival...

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