- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

PT-symmetry-breaking phase transitions in a Lipkin-Meshkov-Glick dimer

Simon Kothe, Christopher Oliver, and Peter Kirton

PDF

Phys. Rev. A 114, 043715 – Published 13 October, 2026

DOI: https://doi.org/10.1103/d2px-dstr

Abstract

The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analog of a parity-time reversal symmetry breaking transition we analyze the steady state phase diagram of a pair of coupled LMG models. Their competition generates a complex phase diagram with multiple steady-state phases and emergent dynamical regimes absent from either constituent model, including chaos characterized by the maximum Lyapunov exponent. We show that the effects predicted from mean-field theory survive in the full quantum model.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. R. Fazio, J. Keeling, L. Mazza, and M. Schirò, Many-body open quantum systems, SciPost Phys. Lect. Notes, 99 (2025).
  2. E. M. Kessler, G. Giedke, A. Imamoglu, S. F. Yelin, M. D. Lukin, and J. I. Cirac, Dissipative phase transition in a central spin system, Phys. Rev. A 86, 012116 (2012).
  3. F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018).
  4. M. Soriente, T. L. Heugel, K. Omiya, R. Chitra, and O. Zilberberg, Distinctive class of dissipation-induced phase transitions and their universal characteristics, Phys. Rev. Res. 3, 023100 (2021).
  5. B. Debecker, J. Martin, and F. Damanet, Spectral theory of non-Markovian dissipative phase transitions, Phys. Rev. A 110, 042201 (2024).
  6. J. Hannukainen and J. Larson, Dissipation-driven quantum phase transitions and symmetry breaking, Phys. Rev. A 98, 042113 (2018).
  7. A. Altland, M. Fleischhauer, and S. Diehl, Symmetry classes of open fermionic quantum matter, Phys. Rev. X 11, 021037 (2021).
  8. K. Kawabata, A. Kulkarni, J. Li, T. Numasawa, and S. Ryu, Symmetry of open quantum systems: Classification of dissipative quantum chaos, PRX Quantum 4, 030328 (2023).
  9. L. Sá, P. Ribeiro, and T. Prosen, Symmetry classification of many-body Lindbladians: Tenfold way and beyond, Phys. Rev. X 13, 031019 (2023).
  10. B. Debecker, L. Pausch, J. Louvet, T. Bastin, J. Martin, and F. Damanet, Role of non-Markovian dissipation in quantum phase transitions: Tricriticality, spin squeezing, and directional symmetry breaking, Phys. Rev. A 112, 012210 (2025).
  11. K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature (London) 464, 1301 (2010).
  12. M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan, Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion, Nat. Commun. 12, 1126 (2021).
  13. Q.-M. Chen, M. Fischer, Y. Nojiri, M. Renger, E. Xie, M. Partanen, S. Pogorzalek, K. G. Fedorov, A. Marx, F. Deppe, et al., Quantum behavior of the Duffing oscillator at the dissipative phase transition, Nat. Commun. 14, 2896 (2023).
  14. S. R. K. Rodriguez, W. Casteels, F. Storme, N. Carlon Zambon, I. Sagnes, L. Le Gratiet, E. Galopin, A. Lemaître, A. Amo, C. Ciuti, and J. Bloch, Probing a dissipative phase transition via dynamical optical hysteresis, Phys. Rev. Lett. 118, 247402 (2017).
  15. G. Beaulieu, F. Minganti, S. Frasca, V. Savona, S. Felicetti, R. Di Candia, and P. Scarlino, Observation of first-and second-order dissipative phase transitions in a two-photon driven Kerr resonator, Nat. Commun. 16, 1954 (2025).
  16. F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009).
  17. M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: A new paradigm for universal quantum computation, New J. Phys. 16, 045014 (2014).
  18. D.-S. Ding, Z.-K. Liu, B.-S. Shi, G.-C. Guo, K. Mølmer, and C. S. Adams, Enhanced metrology at the critical point of a many-body Rydberg atomic system, Nat. Phys. 18, 1447 (2022).
  19. G. Salvatori, A. Mandarino, and M. G. A. Paris, Quantum metrology in Lipkin-Meshkov-Glick critical systems, Phys. Rev. A 90, 022111 (2014).
  20. M. H. Muñoz Arias, I. H. Deutsch, and P. M. Poggi, Phase-space geometry and optimal state preparation in quantum metrology with collective spins, PRX Quantum 4, 020314 (2023).
  21. Y.-H. Ma, S.-H. Su, and C.-P. Sun, Quantum thermodynamic cycle with quantum phase transition, Phys. Rev. E 96, 022143 (2017).
  22. B. M. Garraway, The Dicke model in quantum optics: Dicke model revisited, Philos. Trans. R. Soc. A 369, 1137 (2011).
  23. P. Kirton, M. M. Roses, J. Keeling, and E. G. Dalla Torre, Introduction to the Dicke model: From equilibrium to nonequilibrium, and vice versa, Adv. Quantum Technol. 2, 1800043 (2019).
  24. S. Morrison and A. S. Parkins, Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model with proposed realization in optical cavity QED, Phys. Rev. Lett. 100, 040403 (2008).
  25. S. Morrison and A. S. Parkins, Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement, Phys. Rev. A 77, 043810 (2008).
  26. J. S. Ferreira and P. Ribeiro, Lipkin-Meshkov-Glick model with Markovian dissipation: A description of a collective spin on a metallic surface, Phys. Rev. B 100, 184422 (2019).
  27. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  28. F. Carollo, E. Gillman, H. Weimer, and I. Lesanovsky, Critical behavior of the quantum contact process in one dimension, Phys. Rev. Lett. 123, 100604 (2019).
  29. E. Gillman, F. Carollo, and I. Lesanovsky, Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state, New J. Phys. 21, 093064 (2019).
  30. F. Carollo and I. Lesanovsky, Nonequilibrium dark space phase transition, Phys. Rev. Lett. 128, 040603 (2022).
  31. F. Iemini, A. Russomanno, J. Keeling, M. Schirò, M. Dalmonte, and R. Fazio, Boundary time crystals, Phys. Rev. Lett. 121, 035301 (2018).
  32. T. Prosen, PT-symmetric quantum Liouvillean dynamics, Phys. Rev. Lett. 109, 090404 (2012).
  33. T. Prosen, Generic examples of PT-symmetric qubit (spin-1/2) Liouvillian dynamics, Phys. Rev. A 86, 044103 (2012).
  34. J. Huber, P. Kirton, S. Rotter, and P. Rabl, Emergence of PT-symmetry breaking in open quantum systems, SciPost Phys. 9, 052 (2020).
  35. J. Huber, P. Kirton, and P. Rabl, Nonequilibrium magnetic phases in spin lattices with gain and loss, Phys. Rev. A 102, 012219 (2020).
  36. Y. Nakanishi and T. Sasamoto, PT phase transition in open quantum systems with Lindblad dynamics, Phys. Rev. A 105, 022219 (2022).
  37. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  38. I. I. Arkhipov, A. Miranowicz, F. Minganti, and F. Nori, Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory, Phys. Rev. A 101, 013812 (2020).
  39. H. Lipkin, N. Meshkov, and A. Glick, Validity of many-body approximation methods for a solvable model: (I). Exact solutions and perturbation theory, Nucl. Phys. 62, 188 (1965).
  40. E. Fiorelli, M. Müller, I. Lesanovsky, and F. Carollo, Mean-field dynamics of open quantum systems with collective operator-valued rates: Validity and application, New J. Phys. 25, 083010 (2023).
  41. P. Fowler-Wright, K. B. Arnardóttir, P. Kirton, B. W. Lovett, and J. Keeling, Determining the validity of cumulant expansions for central spin models, Phys. Rev. Res. 5, 033148 (2023).
  42. Note that this is different to the condition imposed by the conservation of total angular momentum 〈(SAx)2〉+〈(SAy)2〉+〈(SAz)2〉=S(S+1), which is true for any state.
  43. T. Tilma, M. J. Everitt, J. H. Samson, W. J. Munro, and K. Nemoto, Wigner functions for arbitrary quantum systems, Phys. Rev. Lett. 117, 180401 (2016).
  44. G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory, Meccanica 15, 9 (1980).
  45. K. Geist, U. Parlitz, and W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Prog. Theor. Phys. 83, 875 (1990).
  46. G. Datseris, DynamicalSystems.jl: A Julia software library for chaos and nonlinear dynamics, J. Open Source Softw. 3, 598 (2018).
  47. P. Solanki and F. Minganti, Chaos as a manifestation of time-translation symmetry breaking, Phys. Rev. B 112, 134311 (2025).
  48. E. Champion, A. Schwartz, M. A. Ijaz, X. Xu, S. Campbell, G. T. Landi, and M. S. Blok, Analog quantum simulation of the Lipkin-Meshkov-Glick model in a transmon qudit, arXiv:2512.05237.
  49. V. Makhalov, T. Satoor, A. Evrard, T. Chalopin, R. Lopes, and S. Nascimbene, Probing quantum criticality and symmetry breaking at the microscopic level, Phys. Rev. Lett. 123, 120601 (2019).
  50. K. Xu, Z.-H. Sun, W. Liu, Y.-R. Zhang, H. Li, H. Dong, W. Ren, P. Zhang, F. Nori, D. Zheng, H. Fan, and H. Wang, Probing dynamical phase transitions with a superconducting quantum simulator, Sci. Adv. 6, eaba4935 (2020).
  51. R. Chinnarasu, C. Poole, L. Phuttitarn, A. Noori, T. M. Graham, S. N. Coppersmith, A. B. Balantekin, and M. Saffman, Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer, PRX Quantum 6, 020350 (2025).
  52. P. M. Harrington, E. J. Mueller, and K. W. Murch, Engineered dissipation for quantum information science, Nat. Rev. Phys. 4, 660 (2022).
  53. C. Oliver, S. Kothe, and  P. Kirton, Data for: “PT-symmetry-breaking phase transitions in a Lipkin-Meshkov-Glick dimer” [Dataset], University of Strathclyde, 2026, https://doi.org/10.15129/99C2D823-05DC-4354-A22F-5097AD9B7AFB.

Outline

Information

Phys. Rev. A 114, 043715– Published 13 October, 2026
  • Received 12 May 2025
  • Revised 6 July 2026
  • Accepted 13 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation