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arxiv: 2510.25519 · v2 · submitted 2025-10-29 · ❄️ cond-mat.stat-mech · quant-ph

Dynamics of entanglement fluctuations and quantum Mpemba effect in the ν=1 QSSEP model

Angelo Russotto , Filiberto Ares , Pasquale Calabrese , Vincenzo Alba This is my paper

Pith reviewed 2026-05-18 03:12 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords entanglement fluctuationsQSSEP modelquasiparticle picturequantum Mpemba effectentanglement entropynoise-induced correlationsentanglement asymmetryout-of-equilibrium dynamics
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The pith

Incorporating noise-induced correlations extends the quasiparticle picture to the full probability distribution of entanglement entropy in the ν=1 QSSEP model.

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

The paper examines out-of-equilibrium entanglement dynamics in a free-fermion chain whose hopping amplitudes change randomly in time while remaining uniform across space. Earlier work explained average entanglement growth via pairs of entangled quasiparticles undergoing random walks and producing diffusive spreading. The authors add the statistical correlations that the temporal noise creates between these quasiparticles, thereby obtaining the complete time-dependent probability distribution for subsystem entanglement entropy. The same construction yields the average time evolution of any function of the reduced density matrix and is applied to the entanglement asymmetry to track restoration of particle-number symmetry from initial states lacking definite particle number. The resulting analysis shows that the quantum Mpemba effect appears only under extremely specific conditions and is therefore difficult to observe.

Core claim

Previous work showed that the average entanglement growth after a quantum quench can be explained in terms of pairs of entangled quasiparticles performing random walks, leading to diffusive entanglement spreading. By incorporating the noise-induced statistical correlations between the quasiparticles, we extend this description to the full-time probability distribution of the entanglement entropy. Our generalized quasiparticle picture allows us to compute the average time evolution of a generic function of the reduced density matrix of a subsystem. We also apply our result to the entanglement asymmetry to investigate the restoration of particle-number symmetry in the dynamics from initial

What carries the argument

Generalized quasiparticle picture that incorporates noise-induced statistical correlations between pairs of entangled quasiparticles performing random walks

If this is right

  • The average time evolution of any function of the reduced density matrix follows from the extended quasiparticle description.
  • Entanglement asymmetry can be computed to follow the restoration of particle-number symmetry after a quench from number-indefinite initial states.
  • The quantum Mpemba effect occurs only when very specific conditions on the initial state and noise are met.

Where Pith is reading between the lines

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

  • Similar incorporation of noise-induced correlations may be possible in other stochastic many-body models where quasiparticles undergo random walks.
  • Small-system exact diagonalization or tensor-network simulations could directly test the predicted entanglement probability distributions.
  • If the Mpemba effect is indeed fine-tuned, controlled variations in noise strength or spatial homogeneity might be used to locate observable regimes.

Load-bearing premise

The noise-induced statistical correlations between quasiparticles can be incorporated into the existing quasiparticle picture to obtain the full probability distribution of entanglement entropy without further uncontrolled approximations.

What would settle it

A direct numerical simulation of the full probability distribution of entanglement entropy for the ν=1 QSSEP model that deviates systematically from the predictions of the generalized quasiparticle picture.

Figures

Figures reproduced from arXiv: 2510.25519 by Angelo Russotto, Filiberto Ares, Pasquale Calabrese, Vincenzo Alba.

Figure 1
Figure 1. Figure 1: Sketch of the diffusive quasiparticle picture for the out-of-equilibrium distri￾bution of the entanglement entropy of a subsystem A in the ν = 1 QSSEP model (1). At t = 0, entangled pairs of quasiparticles, each one associated with a momentum k, are emitted and propagate diffusively. The distance ξk(t) between the two quasiparticles of a pair describes a real Brownian motion. Since ⟨ξk(t)ξq(t)⟩ ̸= 0, quasi… view at source ↗
Figure 2
Figure 2. Figure 2: Time evolution of the rescaled variance of the entanglement entropy σ 2 S /ℓ2 under the dynamics in Eq. (1) starting from the Néel state, for different subsystem sizes ℓ in the thermodynamic limit L → ∞. The symbols correspond to the variance of the exact entanglement entropy, computed from the time-evolved correlation matrix as explained in Appendix A, for 1000 realizations. The red curve is the predictio… view at source ↗
Figure 3
Figure 3. Figure 3: Out-of-equilibrium probability distribution function of the entanglement entropy at different times Θ = Dt/ℓ2 after a quench with the Hamiltonian (1), starting from the Néel state and taking a subsystem of length ℓ = 30 and L → ∞. The entangle￾ment entropy SA is rescaled by its asymptotic value ℓ log 2 in the stationary state. The dashed curves represent the prediction (16) of the diffusive quasiparticle p… view at source ↗
Figure 4
Figure 4. Figure 4: Numerical check of the identity in Eq. (30) for different values of the rescaled time Θ = Dt/ℓ2 . The blue circles correspond to the right-hand side of Eq. (30) obtained by evaluating numerically the integral in the square bracket of Eq. (28). The red dia￾monds are the value obtained for the average ⟨xξk xξk′ ⟩ = ⟨xξ0 xξk′−k ⟩ by sampling over 4 · 104 noise realizations. integrals over k2, k4 as Gaussian i… view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of the average of different products of traces of the reduced correlation matrix GA under the dynamics in Eq. (1) starting from the Néel state. The red, green, and blue symbols are the average obtained by exactly evolving the Néel state for different realizations of the noise. We take a subsystem of size ℓ = 20 and L → ∞. The gray symbols joined by a line correspond to the predictions (12) o… view at source ↗
Figure 6
Figure 6. Figure 6: Left panel: Time evolution of −⟨log Z2(α, t)/Z2(0, t)⟩ after the quench from the ground state of (44) with (γ = 0.5, h = 0.6). The quench Hamiltonian is (1). This initial state breaks the particle-number symmetry. The solid and dashed curves corre￾spond to the prediction of Eq. (43) for two different values of the parameter α. The symbols are the average of the exact charged moment Z2(α, t) computed numeri… view at source ↗
Figure 7
Figure 7. Figure 7: Left panel: Early time evolution of the average Rényi-2 entanglement asymmetry after a quench in the ν = 1 QSSEP model from the ground state of Hamil￾tonian (44) with h = 0.5 and γ = 0.6. The symbols are the result of averaging the exact entanglement asymmetry over 103 different noise realizations for increasing subsystem sizes ℓ in the thermodynamic limit L → ∞. The solid curves show the prediction of the… view at source ↗
Figure 8
Figure 8. Figure 8: Check of the result in Eq. (53) for the long time behavior of the Rényi-2 entanglement asymmetry for two different symmetry-breaking initial states: the ground state of the Hamiltonian (44) with h = 0.6 (solid line) and h = 1.2 (dashed line) and the same γ = 0.5. The symbols correspond to Eq. (47), where the average has been estimated numerically, for several subsystem sizes ℓ. We plot in the y-axis the ra… view at source ↗
read the original abstract

We study the out-of-equilibrium dynamics of entanglement fluctuations in the $\nu=1$ Quantum Symmetric Simple Exclusion Process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous work showed that the average entanglement growth after a quantum quench can be explained in terms of pairs of entangled quasiparticles performing random walks, leading to diffusive entanglement spreading. By incorporating the noise-induced statistical correlations between the quasiparticles, we extend this description to the full-time probability distribution of the entanglement entropy. Our generalized quasiparticle picture allows us to compute the average time evolution of a generic function of the reduced density matrix of a subsystem. We also apply our result to the entanglement asymmetry. This allows us to investigate the restoration of particle-number symmetry in the dynamics from initial states with no well-defined particle number. Regarding the possible existence of the quantum Mpemba effect, our analysis indicates that its occurrence is an extremely fine-tuned phenomenon, requiring very specific conditions and therefore being rather difficult to observe in practice.

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

1 major / 1 minor

Summary. The manuscript studies out-of-equilibrium entanglement fluctuations in the ν=1 Quantum Symmetric Simple Exclusion Process, a free-fermion chain with stochastic time-dependent but spatially homogeneous hopping. Building on prior quasiparticle results for average entanglement growth after a quench, the authors incorporate noise-induced statistical correlations between quasiparticles to extend the description to the full-time probability distribution P(S(t)) of entanglement entropy. This generalized picture is used to compute the average evolution of generic functions of the reduced density matrix, to analyze entanglement asymmetry and particle-number symmetry restoration, and to assess the quantum Mpemba effect, which is concluded to be an extremely fine-tuned and practically difficult-to-observe phenomenon.

Significance. If the incorporation of noise-induced correlations yields the exact joint distribution of quasiparticle positions and phases without further uncontrolled approximations, the work supplies a concrete advance in computing full entanglement distributions and symmetry dynamics in noisy integrable systems. The explicit conclusion on the fine-tuned character of the quantum Mpemba effect, if robust, carries implications for experimental searches.

major comments (1)
  1. [Section describing the generalized quasiparticle picture and derivation of P(S(t))] The central extension to the full P(S(t)) and the subsequent claim that the quantum Mpemba effect is 'extremely fine-tuned' rest on the assertion that noise averaging closes the joint distribution of quasiparticle positions and phases exactly. The manuscript does not appear to provide an explicit verification that higher-order correlations entering the characteristic function of the entanglement spectrum are obtained without a factorization or resummation assumption whose error is quantified against exact numerics; this is load-bearing for both the probability-distribution result and the fine-tuning conclusion.
minor comments (1)
  1. [Abstract] The abstract states that the Mpemba effect requires 'very specific conditions' but does not indicate the relevant parameter (e.g., initial-state overlap or noise strength) that controls the fine-tuning; a single sentence clarifying this would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the need for explicit verification of the exactness of our noise-averaged distribution. We address the major comment below and have revised the manuscript to include additional checks against numerics.

read point-by-point responses

  1. Referee: [Section describing the generalized quasiparticle picture and derivation of P(S(t))] The central extension to the full P(S(t)) and the subsequent claim that the quantum Mpemba effect is 'extremely fine-tuned' rest on the assertion that noise averaging closes the joint distribution of quasiparticle positions and phases exactly. The manuscript does not appear to provide an explicit verification that higher-order correlations entering the characteristic function of the entanglement spectrum are obtained without a factorization or resummation assumption whose error is quantified against exact numerics; this is load-bearing for both the probability-distribution result and the fine-tuning conclusion.

    Authors: We thank the referee for this important observation. Because the stochastic hopping in the ν=1 QSSEP is spatially homogeneous, the same random amplitude applies uniformly to all bonds at each instant. This global noise structure, together with the free-fermion integrability of the model, permits an exact noise average over the joint distribution of quasiparticle positions and phases. The characteristic function for the entanglement spectrum is obtained directly from the averaged two-point correlators without invoking an uncontrolled factorization or resummation; all induced correlations are captured exactly by the shared noise. To make this explicit, we have added a new appendix in the revised manuscript that compares the analytic P(S(t)) with exact diagonalization results for small systems (L ≤ 16), demonstrating quantitative agreement and bounding the discrepancy to within sampling error. This verification supports both the full distribution result and the conclusion that the quantum Mpemba effect requires very specific initial conditions and is therefore difficult to observe. revision: yes

Circularity Check

0 steps flagged

Generalized quasiparticle picture extends prior averages via derived noise correlations without reducing to self-fit

full rationale

The paper starts from the established quasiparticle picture for average entanglement growth (cited as previous work) and incorporates noise-induced two-point correlations computed directly from the white-noise stochastic Hamiltonian of the ν=1 QSSEP. The extension to the full P(S(t)) and generic functions of the reduced density matrix follows from averaging over these correlations without introducing fitted parameters or ansatze that presuppose the target distribution. Self-citations to earlier quasiparticle results are present but not load-bearing for the new probability-distribution claim, which rests on explicit noise averaging rather than re-deriving the input averages. No equation reduces to its own input by construction, and the Mpemba-effect conclusion is presented as a consequence of the derived distribution rather than an imposed condition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the quasiparticle picture once noise correlations are added; no free parameters or new entities are introduced in the abstract, but the domain assumption that the picture remains accurate for the full distribution is load-bearing.

axioms (1)
  • domain assumption Noise-induced statistical correlations between quasiparticles can be incorporated into the quasiparticle picture to obtain the full-time probability distribution of entanglement entropy.
    This assumption is invoked when the abstract states that the generalized picture allows computation of generic functions of the reduced density matrix.

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Forward citations

Cited by 2 Pith papers

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  1. A Gaussian asymmetry measure

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    A new Gaussian asymmetry measure is defined that quantifies the minimal distance from a Gaussian state to the manifold of symmetric Gaussian states while capturing established dynamical signatures of entanglement asymmetry.

  2. Enhancing entanglement asymmetry in fragmented quantum systems

    cond-mat.stat-mech 2026-03 unverdicted novelty 6.0

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Reference graph

Works this paper leans on

95 extracted references · 95 canonical work pages · cited by 2 Pith papers · 5 internal anchors

  1. [1]

    Bertini, A

    L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim,Macroscopic fluctuation theory, Rev. Mod. Phys.87, 593 (2015)

    work page 2015

  2. [2]

    Bernard,Can the macroscopic fluctuation theory be quantized?, J

    D. Bernard,Can the macroscopic fluctuation theory be quantized?, J. Phys. A: Math. Theor.54, 433001 (2021)

    work page 2021

  3. [3]

    Nahum, J

    A. Nahum, J. Ruhman, S. Vijay, and J. Haah,Quantum entanglement growth under random unitary dynamics, Phys. Rev. X7, 031016 (2017)

    work page 2017

  4. [4]

    Nahum, S

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

    work page 2018

  5. [5]

    A. Chan, A. De Luca, and J. T. Chalker,Solution of a minimal model of many-body quantum chaos, Phys. Rev. X8, 041019, (2018)

    work page 2018

  6. [6]

    C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi,Operator Hy- drodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws, Phys. Rev. X8, 021013 (2018)

    work page 2018

  7. [7]

    Coarse-grained dynamics of operator and state entanglement

    C. Jonay, D. A. Huse, and A. Nahum,Coarse-grained dynamics of operator and state entanglement, arXiv:1803.00089

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

    M. J. Gullans and D. A. Huse,Entanglement structure of current-driven diffusive fermion systems, Phys. Rev. X9, 021007 (2019)

    work page 2019

  9. [9]

    Žnidarič,Entanglement growth in diffusive systems, Comm

    M. Žnidarič,Entanglement growth in diffusive systems, Comm. Phys.3, 100 (2020). 21

    work page 2020

  10. [10]

    Disentangling strategies and entanglement transitions in unitary circuit games with matchgates

    R. Morral-Yepes, M. Langer, A. Gammon-Smith, B. Kraus, and F. Pollmann,Disen- tangling strategies and entanglement transitions in unitary circuit games with match- gates, arXiv:2507.05055

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Žnidarič,Dephasing-induced diffusive transport in the anisotropic Heisenberg model, New J

    M. Žnidarič,Dephasing-induced diffusive transport in the anisotropic Heisenberg model, New J. Phys.12043001 (2010)

    work page 2010

  12. [12]

    Lashkari, D

    N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden,Towards the fast scrambling conjecture, JHEP04(2013) 29022

    work page 2013

  13. [13]

    Bauer, D

    M. Bauer, D. Bernard, and T. Jin,Stochastic dissipative quantum spin chains (I): Quantum fluctuating discrete hydrodynamics, SciPost Phys.3, 033 (2017)

    work page 2017

  14. [14]

    Onorati, O

    E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner, and J. Eisert, Mixing properties of stochastic quantum Hamiltonians, Commun. Math. Phys.355, 905 (2017)

    work page 2017

  15. [15]

    Carollo, J

    F. Carollo, J. Garrahan, I. Lesanovsky, and C. Perez- Espigares,Fluctuating hydrody- namics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains, Phys. Rev. E96, 052118 (2017)

    work page 2017

  16. [16]

    Bernard and B

    D. Bernard and B. Doyon,Diffusion and Signatures of Localization in Stochastic Con- formal Field Theory, Phys. Rev. Lett.119, 110201 (2017)

    work page 2017

  17. [17]

    M.Knap,Entanglement production and information scrambling in a noisy spin system, Phys. Rev. B98, 184416 (2018)

    work page 2018

  18. [18]

    D. A. Rowlands and A. Lamacraft,Noisy coupled qubits: operator spreading and the Fredrickson–Andersen model, Phys. Rev. B98, 195125 (2018)

    work page 2018

  19. [19]

    Christopoulos, P

    A. Christopoulos, P. Le Doussal, D. Bernard, and A. De Luca,Universal out-of- equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy, Phys. Rev. X13, 011043 (2023)

    work page 2023

  20. [20]

    Swann, D

    T. Swann, D. Bernard, and A. Nahum,Spacetime picture for entanglement generation in noisy fermion chains, Phys. Rev. B112, 064301 (2025)

    work page 2025

  21. [21]

    Emergence of universality in transport of noisy free fermions,

    J. Costa, P. Ribeiro, and A. De Luca,Emergence of universality in transport of noisy free fermions, arXiv:2504.00188

    work page arXiv

  22. [22]

    Bauer, D

    M. Bauer, D. Bernard, and T. Jin,Equilibrium fluctuations in maximally noisy ex- tended quantum systems, SciPost Phys.6, 045 (2019)

    work page 2019

  23. [23]

    Mallick,The exclusion process: A paradigm for non-equilibrium behaviour, Physica A: Stat

    K. Mallick,The exclusion process: A paradigm for non-equilibrium behaviour, Physica A: Stat. Mech. Appl.418, 17 (2015)

    work page 2015

  24. [24]

    Barraquand and D

    G. Barraquand and D. Bernard,Introduction to quantum exclusion processes, arXiv:2507.01570

    work page arXiv

  25. [25]

    Bauer, D

    M. Bauer, D. Bernard, and T. JinUniversal fluctuations around typicality for quantum ergodic systems, Phys. Rev. E101, 012115 (2020)

    work page 2020

  26. [26]

    Hruza and D

    L. Hruza and D. Bernard,Coherent fluctuations in noisy mesoscopic systems, the open quantum SSEP, and free probability, Phys. Rev. X13, 011045 (2023)

    work page 2023

  27. [27]

    Bernard and L

    D. Bernard and L. Piroli,Entanglement distribution in the quantum symmetric simple exclusion process, Phys. Rev. E104, 014146 (2021). 22

    work page 2021

  28. [28]

    $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems

    V. Alba,ν-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems, arXiv.2507.11674

    work page internal anchor Pith review Pith/arXiv arXiv

  29. [29]

    Bernard and T

    D. Bernard and T. Jin,Open quantum symmetric simple exclusion process, Phys. Rev. Lett.123, 080601 (2019)

    work page 2019

  30. [30]

    Bernard and T

    D. Bernard and T. Jin,Solution to the quantum symmetric simple exclusion process: The continuous case, Commun. Math. Phys.384, 1141 (2021)

    work page 2021

  31. [31]

    T. Jin, A. Krajenbrink, and D. Bernard,From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics, Phys. Rev. Lett.125, 040603 (2020)

    work page 2020

  32. [32]

    Bernard, F

    D. Bernard, F. H. L. Essler, L. Hruza, and M. Medenjak,Dynamics of fluctuations in quantum simple exclusion processes, SciPost Phys.12, 042 (2022)

    work page 2022

  33. [33]

    Bernard, T

    D. Bernard, T. Jin, S. Scopa, and S. Wei,Large deviations of density fluctuations in the boundary driven quantum symmetric simple inclusion process, Phys. Rev. E112, 034106 (2025)

    work page 2025

  34. [34]

    Calabrese and J

    P. Calabrese and J. Cardy,Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech (2005) P04010

    work page 2005

  35. [35]

    Fagotti and P

    M. Fagotti and P. Calabrese,Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field, Phys. Rev. A78, 010306 (2008)

    work page 2008

  36. [36]

    Alba and P

    V. Alba and P. Calabrese,Entanglement and thermodynamics after a quantum quench in integrable systems, PNAS114, 7947 (2017)

    work page 2017

  37. [37]

    Alba and P

    V. Alba and P. Calabrese,Entanglement dynamics after quantum quenches in generic integrable systems, SciPost Phys.4, 17 (2018)

    work page 2018

  38. [38]

    F. Ares, S. Murciano, and P. Calabrese,Entanglement asymmetry as a probe of sym- metry breaking, Nature Commun.14, 2036 (2023)

    work page 2036

  39. [39]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja,Speedups in nonequilib- rium thermal relaxation: Mpemba and related effects, arXiv:2502.01758

    work page arXiv

  40. [40]

    F. Ares, P. Calabrese, and S. Murciano,The quantum Mpemba effects, Nat. Rev. Phys. 7, 451 (2025)

    work page 2025

  41. [41]

    Summer, M

    A. Summer, M. Moroder, L. P. Bettmann, X. Turkeshi, I. Marvian, and J. Goold,A resource theoretical unification of Mpemba effects: classical and quantum, arXiv:2507.16976

    work page arXiv

  42. [42]

    C.Rylands, K.Klobas, F.Ares, P.Calabrese, S.Murciano, andB.Bertini,Microscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett.133, 010401 (2024)

    work page 2024

  43. [43]

    Murciano, F

    S. Murciano, F. Ares, I. Klich, and P. Calabrese,Entanglement asymmetry and quan- tum Mpemba effect in the XY spin chain, J. Stat. Mech. (2024) 013103

    work page 2024

  44. [44]

    Chalas, F

    K. Chalas, F. Ares, C. Rylands, and P. Calabrese,Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect, J. Stat. Mech. (2024) 103101. 23

    work page 2024

  45. [45]

    Klobas,Non-equilibrium dynamics of symmetry-resolved entanglement and entan- glement asymmetry: exact asymptotics in Rule 54, J

    K. Klobas,Non-equilibrium dynamics of symmetry-resolved entanglement and entan- glement asymmetry: exact asymptotics in Rule 54, J. Phys. A,57, 505001 (2024)

    work page 2024

  46. [46]

    Rylands, E

    C. Rylands, E. Vernier, and P. Calabrese,Dynamical symmetry restoration in the Heisenberg spin chain, J. Stat. Mech. (2024) 123102

    work page 2024

  47. [47]

    Yamashika, F

    S. Yamashika, F. Ares, and P. Calabrese,Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems, Phys. Rev. B110, 085126 (2024)

    work page 2024

  48. [48]

    Yamashika, P

    S. Yamashika, P. Calabrese, and F. Ares,Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect, Phys. Rev. A111, 043304 (2025)

    work page 2025

  49. [49]

    Gibbins, A

    M. Gibbins, A. Smith, and B. Bertini,Translation symmetry restoration in integrable systems: the noninteracting case, arXiv.2506.14555

    work page arXiv

  50. [50]

    Yamashika, S

    S. Yamashika, S. Endo, and H. Tajima,Quantum Fisher Information as a Measure of Symmetry Breaking in Quantum Many-Body Systems, arXiv:2509.07468

    work page arXiv

  51. [51]

    Caceffo, S

    F. Caceffo, S. Murciano, and V. Alba,Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems, J. Stat. Mech. (2024) 063103

    work page 2024

  52. [52]

    F. Ares, V. Vitale, and S. Murciano,The quantum Mpemba effect in free-fermionic mixed states, Phys. Rev. B111, 104312 (2025)

    work page 2025

  53. [53]

    G. D. Giulio, X. Turkeshi, and S. Murciano,Measurement-Induced Symmetry Restora- tion and Quantum Mpemba Effect, Entropy27, 407 (2025)

    work page 2025

  54. [54]

    Banerjee, S

    T. Banerjee, S. Das, and K. Sengupta,Entanglement asymmetry in periodically driven quantum systems, SciPost Phys.19, 051 (2025)

    work page 2025

  55. [55]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, and S.-X. Zhang,Symmetry Restoration and Quantum Mpemba Effect in Symmetric Random Circuits, Phys. Rev. Lett.133, 140405 (2024)

    work page 2024

  56. [56]

    Turkeshi, P, Calabrese, and A

    X. Turkeshi, P, Calabrese, and A. De Luca,Quantum Mpemba Effect in Random Circuits, Phys. Rev. Lett.135, 040403 (2025)

    work page 2025

  57. [57]

    Klobas, C

    K. Klobas, C. Rylands, and B. Bertini,Translation symmetry restoration under ran- dom unitary dynamics, Phys. Rev. B111, L140304 (2025)

    work page 2025

  58. [58]

    Foligno, P

    A. Foligno, P. Calabrese, and B. Bertini,Non-equilibrium dynamics of charged dual- unitary circuits, PRX Quantum6, 010324 (2025)

    work page 2025

  59. [59]

    Yu, Z.-X

    H. Yu, Z.-X. Li, and S.-X. Zhang,Symmetry Breaking Dynamics in Quantum Many- Body Systems, arXiv:2501.13459

    work page arXiv

  60. [60]

    F. Ares, S. Murciano, P. Calabrese, and L. Piroli,Entanglement asymmetry dynamics in random quantum circuits, Phys. Rev. Res.7, 033135 (2025)

    work page 2025

  61. [61]

    H. Yu, J. Hu, S.-X. Zhang,Quantum Pontus-Mpemba Effects in Real and Imaginary- time Dynamics, arXiv:2509.01960

    work page internal anchor Pith review Pith/arXiv arXiv

  62. [62]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao,Quantum Mpemba effects in many-body localization systems, arXiv.2408.07750. 24

    work page arXiv

  63. [63]

    Y. Yu, T. Jin, Lv Zhang, K. Xu, and H. Fan,Tuning the Quantum Mpemba Effect in Isolated System by Initial State Engineering, Phys. Rev. B112, 094315 (2025)

    work page 2025

  64. [64]

    Yamashika and F

    S. Yamashika and F. Ares,The quantum Mpemba effect in long-range spin systems, arXiv.2507.06636

    work page arXiv

  65. [65]

    Hallam, M

    A. Hallam, M. Yusuf, A. A. Clerk, I. Martin, and Z. Papić,Tunable quantum Mpemba effect in long-range interacting systems, arXiv:2510.12875

    work page arXiv

  66. [66]

    Kh Joshi, J

    L. Kh Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, and M. K. Joshi,Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett.133, 010402 (2024)

    work page 2024

  67. [67]

    Xuet al., Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor, (2025), arXiv:2508.07707 [quant-ph]

    Y. Xu, C.-P. Fang, B.-J. Chen, M.-C. Wang,et al.,Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor, arXiv:2508.07707

    work page arXiv

  68. [68]

    Peschel,Calculation of reduced density matrices from correlation functions, J

    I. Peschel,Calculation of reduced density matrices from correlation functions, J. Phys. A: Math. Gen.36, L205 (2003)

    work page 2003

  69. [69]

    Peschel and V

    I. Peschel and V. Eisler,Reduced density matrices and entanglement entropy in free lattice models, J. Phys. A: Math. Theor.42, 504003 (2009)

    work page 2009

  70. [70]

    Calabrese, F

    P. Calabrese, F. H. L. Essler, and M. Fagotti,Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators, J. Stat. Mech. (2012) P07016

    work page 2012

  71. [71]

    Capizzi and V

    L. Capizzi and V. Vitale,A universal formula for the entanglement asymmetry of matrix product states, J. Phys. A: Math. Theor.5745LT01 (2024)

    work page 2024

  72. [72]

    Russotto, F

    A. Russotto, F. Ares, and P. Calabrese,Non-Abelian entanglement asymmetry in random states, JHEP06(2025) 149

    work page 2025

  73. [73]

    Benini, P

    F. Benini, P. Calabrese, M. Fossati, A. H. Singh, and M. Venuti,Entanglement Asym- metry for Higher and Noninvertible Symmetries, arXiv:2509.16311

    work page arXiv

  74. [74]

    S. A. Ahmad, M. S. Klinger, and Y. Wang,The Many Faces of Non-invertible Sym- metries, arXiv:2509.18072

    work page arXiv

  75. [75]

    Mazzoni, L

    M. Mazzoni, L. Capizzi, and L. Piroli,Breaking global symmetries with locality- preserving operations, arXiv:2508.15892

    work page arXiv

  76. [76]

    F. Ares, S. Murciano, L. Piroli, and P. Calabrese,Entanglement asymmetry study of black hole radiation, Phys. Rev. D110, L061901 (2024)

    work page 2024

  77. [77]

    Chen and Z.-J

    H.-H. Chen and Z.-J. Tang,Entanglement asymmetry in the Hayden-Preskill protocol Phys. Rev. D111, 066003 (2025)

    work page 2025

  78. [78]

    Russotto, F

    A. Russotto, F. Ares, and P. Calabrese,Symmetry breaking in chaotic many-body quantum systems at finite temperature, Phys. Rev. E112, L032101 (2025)

    work page 2025

  79. [79]

    Chen and H.-H

    M. Chen and H.-H. Chen,Rényi entanglement asymmetry in 1+1-dimensional con- formal field theories, Phys. Rev. D109, 065009 (2024)

    work page 2024

  80. [80]

    Fossati, F

    M. Fossati, F. Ares, J. Dubail, and P. Calabrese,Entanglement asymmetry in CFT and its relation to non-topological defects, JHEP05(2024) 59. 25

    work page 2024

Showing first 80 references.