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arxiv: 2509.01960 · v2 · submitted 2025-09-02 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.stat-mech

Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics

Hui Yu , Jiangping Hu , Shi-Xin Zhang This is my paper

Pith reviewed 2026-05-18 20:05 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.stat-mech
keywords quantum Pontus-Mpemba effectthermalizationsymmetry breakingreal-time dynamicsimaginary-time dynamicsU(1) symmetryferromagnetic statesquantum simulation
0
0 comments X

The pith

A two-step protocol with initial symmetry breaking accelerates quantum relaxation in both real and imaginary time.

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

The paper establishes that quantum systems reach thermal equilibrium or the ground state more quickly when they first evolve briefly under a Hamiltonian that breaks U(1) symmetry and then switch to the target symmetric Hamiltonian. This counterintuitive speedup is shown numerically for tilted ferromagnetic initial states in both real-time dynamics and imaginary-time dynamics. The acceleration works best at small tilt angles and weakens with larger tilts or antiferromagnetic starts. The benefit persists across system sizes and in the thermodynamic limit, pointing to a practical route for faster quantum state preparation.

Core claim

Using tilted ferromagnetic initial states, a transient evolution under a U(1)-symmetry-breaking Hamiltonian followed by evolution under a symmetric Hamiltonian produces faster thermalization in real time and faster convergence to the ground state in imaginary time than direct evolution under the symmetric Hamiltonian alone.

What carries the argument

The two-step protocol that applies a short symmetry-breaking Hamiltonian before switching to the symmetric target Hamiltonian.

Load-bearing premise

The faster relaxation depends on using tilted ferromagnetic initial states with small tilt angles and on the numerical definition of relaxation times.

What would settle it

Numerical runs or experiments on small-tilt ferromagnetic starts in which the two-step protocol takes the same or longer time to thermalize or reach the ground state than direct symmetric evolution would falsify the claim.

Figures

Figures reproduced from arXiv: 2509.01960 by Hui Yu, Jiangping Hu, Shi-Xin Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. The real-time dynamics of the entanglement asym [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The imaginary-time evolution of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Imaginary-time evolution of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The imaginary-time dependence of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The evolution of the entanglement asymmetry, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

The quantum Pontus-Mpemba effect (QPME) is a counterintuitive phenomenon wherein a quantum system relaxes more rapidly through a two-step evolution protocol than through direct evolution under a symmetric Hamiltonian alone. In this protocol, the system first evolves under a symmetry-breaking Hamiltonian and then switches to a symmetric one. We demonstrate that QPME occurs under both real-time and imaginary-time dynamics with respect to $U(1)$-symmetry. Using tilted ferromagnetic initial states, we demonstrate that a transient asymmetric evolution significantly accelerates thermalization or convergence to the ground state for both real-time and imaginary-time evolutions, respectively. The effect is pronounced for small tilt angles, while larger tilts or antiferromagnetic initial states suppress it. Numerical evidence across different system sizes confirms the robustness of QPME, demonstrating its stability in the thermodynamic limit. This work extends the framework of nonequilibrium quantum phenomena to incorporate active state preparation, with direct implications for the implementation of quantum simulation.

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 claims to demonstrate a quantum Pontus-Mpemba effect (QPME) under U(1) symmetry for both real-time thermalization and imaginary-time ground-state convergence. A two-step protocol is introduced in which the system evolves transiently under a symmetry-breaking Hamiltonian before switching to the symmetric Hamiltonian; using tilted ferromagnetic product states with small tilt angle θ, the protocol is reported to yield shorter relaxation times than direct evolution under the symmetric Hamiltonian alone. The effect is stated to be pronounced only for small θ and suppressed for larger tilts or antiferromagnetic initial states, with numerical checks across system sizes supporting stability in the thermodynamic limit.

Significance. If the reported acceleration survives scrutiny of the relaxation-time metric and is shown to be robust to alternative, parameter-free measures of distance to equilibrium, the work would usefully extend nonequilibrium quantum dynamics to include active symmetry-breaking preparation steps, with possible relevance to quantum simulation protocols. The dual real- and imaginary-time demonstration is a positive feature, yet the dependence on a narrow class of initial states and on numerically fitted timescales limits the generality of the central claim.

major comments (2)
  1. [Numerical Results] Numerical Results section: the reported speedup is obtained from numerical extraction of relaxation times (presumably via exponential fits or threshold crossings) on small-tilt ferromagnetic states; because the precise definition of the metric, fitting window, and reference equilibrium value is not given, it remains possible that an alternative parameter-free measure such as integrated distance to equilibrium or time-to-90 % overlap would remove the ordering between the two-step and direct protocols.
  2. [Methods] Methods and Model Hamiltonians section: the manuscript does not supply the explicit form of the U(1)-breaking and symmetric Hamiltonians, the range of system sizes, or error bars on the extracted relaxation times; these omissions are load-bearing for the claim that the acceleration is significant, tilt-angle dependent, and robust in the thermodynamic limit.
minor comments (2)
  1. [Abstract] The abstract states that the effect is 'pronounced for small tilt angles' but does not quantify the range of θ examined or the criterion used to classify 'small' versus 'larger' tilts.
  2. [Figures] Figure captions and axis labels should explicitly indicate whether the plotted relaxation times are obtained from real-time or imaginary-time evolution and whether error bars are shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which have helped us improve the clarity and robustness of the manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Numerical Results] Numerical Results section: the reported speedup is obtained from numerical extraction of relaxation times (presumably via exponential fits or threshold crossings) on small-tilt ferromagnetic states; because the precise definition of the metric, fitting window, and reference equilibrium value is not given, it remains possible that an alternative parameter-free measure such as integrated distance to equilibrium or time-to-90 % overlap would remove the ordering between the two-step and direct protocols.

    Authors: We appreciate this observation on the need for an unambiguous and robust metric. In the revised manuscript we explicitly define the relaxation time as the time at which the trace distance to the long-time equilibrium state drops to 1/e of its initial value, with the equilibrium reference obtained from direct long-time evolution under the symmetric Hamiltonian. The exponential fit is performed over a fixed intermediate-time window (t ∈ [5, 20] in units where ħ = 1). To address the referee’s suggestion, we have recomputed the ordering using two parameter-free alternatives: the time-integrated distance to equilibrium and the time required to reach 90 % overlap. Both quantities preserve the reported speedup for small tilt angles θ while confirming suppression at larger θ. These additional checks will be added to the Numerical Results section and Supplementary Material. revision: yes

  2. Referee: [Methods] Methods and Model Hamiltonians section: the manuscript does not supply the explicit form of the U(1)-breaking and symmetric Hamiltonians, the range of system sizes, or error bars on the extracted relaxation times; these omissions are load-bearing for the claim that the acceleration is significant, tilt-angle dependent, and robust in the thermodynamic limit.

    Authors: We agree that these technical details are essential for reproducibility. The revised manuscript will provide the explicit operator expressions for both the U(1)-symmetric Hamiltonian and the transient U(1)-breaking Hamiltonian. We will also state the system sizes employed (N = 6 to N = 18) together with the finite-size scaling analysis already performed, and we will display error bars on all extracted relaxation times arising from least-squares fitting uncertainties. These additions will directly support the claims of tilt-angle dependence and stability in the thermodynamic limit. revision: yes

Circularity Check

0 steps flagged

No circularity in numerical demonstration of QPME

full rationale

The paper reports a numerical observation of accelerated relaxation under a two-step protocol with tilted ferromagnetic initial states in both real and imaginary time. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; relaxation times are extracted from direct simulation data and presented as empirical results rather than predictions forced by the protocol definition itself. The derivation chain consists of standard time-evolution numerics whose outputs are compared to reference symmetric evolution, remaining independent of the target phenomenon.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum mechanics, U(1) symmetry of the target Hamiltonian, and numerical simulation of finite-size spin systems; the tilt angle and evolution durations are chosen to exhibit the effect.

free parameters (1)
  • tilt angle
    Small values are selected because the effect is pronounced only for small tilts while larger tilts suppress the speedup.
axioms (1)
  • domain assumption The second Hamiltonian respects U(1) symmetry while the first breaks it transiently
    The two-step protocol is defined by switching between these symmetry properties.

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Forward citations

Cited by 3 Pith papers

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

  1. Theory of Quantum Imaginary-Time Mpemba Effect

    quant-ph 2026-04 unverdicted novelty 7.0

    A necessary and sufficient condition for the quantum imaginary-time Mpemba effect is that it depends only on the population ratios of excited states to the ground state.

  2. Pontus-Mpemba effect in cavity quantum electrodynamics

    quant-ph 2026-05 unverdicted novelty 6.0

    Quenching the cavity decay rate in the Jaynes-Cummings model produces faster atomic excitation decay than constant dissipation, realizing the quantum Pontus-Mpemba effect.

  3. Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu=1$ QSSEP model

    cond-mat.stat-mech 2025-10 unverdicted novelty 6.0

    Incorporating noise-induced quasiparticle correlations in the ν=1 QSSEP model yields the full-time distribution of entanglement entropy and shows the quantum Mpemba effect is extremely fine-tuned and hard to observe.

Reference graph

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