- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Long-range interacting many-body systems in the irrep basis

Ivy Pannier-Günther1,*, Andrew Kolmer Forbes1,†, Pablo M. Poggi1,2, and Ivan H. Deutsch1

  • *Contact author: igunther@unm.edu
  • †Contact author: aforbes@unm.edu
PDF

Phys. Rev. Research 7, 043056 – Published 15 October, 2025

DOI: https://doi.org/10.1103/w12m-9f2s

Abstract

Spin models featuring infinite-range, homogeneous all-to-all interactions can be efficiently described due to the existence of a symmetry-restricted Hilbert subspace and an underlying classical phase-space structure. However, when the permutation invariance of the system is weakly broken, such as by long- but finite-range interactions, these tools become mathematically invalid. Here, we propose to approximately describe these scenarios by considering additional many-body subspaces according to the hierarchy of their coupling to the symmetric subspace, defined by leveraging the structure of irreducible representations (irreps) of the group SU(2). We put forward a procedure, dubbed “irrep distillation,” which defines these additional subspaces to minimize their dimension at each order of approximation. We discuss the validity of our method in connection with the occurrence of quantum many-body scars, benchmark its utility by analyzing the dynamical and equilibrium phase transitions, outline its phenomenology, and compare its use-cases against other approximations of long-range many-body systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. 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).
  2. M. Tavis and F. W. Cummings, Exact solution for an n-molecule—radiation-field Hamiltonian, Phys. Rev. 170, 379 (1968).
  3. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  4. A. N. Ivanov and O. I. Motrunich, Volume-entangled exact eigenstates in the PXP and related models in any dimension, Phys. Rev. Lett. 134, 050403 (2025).
  5. E. Ising, Contribution to the theory of ferromagnetism, Z. Phys. 31, 253 (1925).
  6. A. Russomanno, M. Fava, and M. Heyl, Quantum chaos and ensemble inequivalence of quantum long-range Ising chains, Phys. Rev. B 104, 094309 (2021).
  7. H. Kim, T. N. Ikeda, and D. A. Huse, Testing whether all eigenstates obey the eigenstate thermalization hypothesis, Phys. Rev. E 90, 052105 (2014).
  8. R. Mattes, I. Lesanovsky, and F. Carollo, Long-range interacting systems are locally noninteracting, Phys. Rev. Lett. 134, 070402 (2025).
  9. A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Theory of robust quantum many-body scars in long-range interacting systems, Phys. Rev. X 15, 011020 (2025).
  10. J. M. Deutsch, Eigenstate thermalization hypothesis, Rep. Prog. Phys. 81, 082001 (2018).
  11. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  12. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  13. M. Kac and C. J. Thompson, Critical behavior of several lattice models with long‐range interaction, J. Math. Phys. 10, 1373 (1969).
  14. D. Porras and J. I. Cirac, Effective quantum spin systems with trapped ions, Phys. Rev. Lett. 92, 207901 (2004).
  15. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature (London) 534, 667 (2016).
  16. J. Schachenmayer, B. Lanyon, C. Roos, and A. Daley, Entanglement growth in quench dynamics with variable range interactions, Phys. Rev. X 3, 031015 (2013).
  17. P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Non-local propagation of correlations in quantum systems with long-range interactions, Nature (London) 511, 198 (2014).
  18. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
  19. S. Pappalardi, A. Russomanno, B. Žunkovič, F. Iemini, A. Silva, and R. Fazio, Scrambling and entanglement spreading in long-range spin chains, Phys. Rev. B 98, 134303 (2018).
  20. B. Žunkovič, M. Heyl, M. Knap, and A. Silva, Dynamical quantum phase transitions in spin chains with long-range interactions: Merging different concepts of nonequilibrium criticality, Phys. Rev. Lett. 120, 130601 (2018).
  21. N. Defenu, A. Lerose, and S. Pappalardi, Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions, Phys. Rep. 1074, 1 (2024).
  22. 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).
  23. M. Heyl, F. Pollmann, and B. Dóra, Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators, Phys. Rev. Lett. 121, 016801 (2018).
  24. R. Khasseh, A. Russomanno, M. Schmitt, M. Heyl, and R. Fazio, Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench, Phys. Rev. B 102, 014303 (2020).
  25. M. H. Muñoz Arias, I. H. Deutsch, P. S. Jessen, and P. M. Poggi, Simulation of the complex dynamics of mean-field p-spin models using measurement-based quantum feedback control, Phys. Rev. A 102, 022610 (2020).
  26. A. Mitra, T. Albash, P. D. Blocher, J. Takahashi, A. Miyake, G. W. Biedermann, and I. H. Deutsch, Macrostates vs. microstates in the classical simulation of critical phenomena in quench dynamics of 1D Ising models, New J. Phys. 27, 013026 (2025).
  27. K. R. Chinni, Reliability of quantum simulation on NISQ-era devices, Ph.D. thesis, University of New Mexico, 2022.
  28. T. Comparin, F. Mezzacapo, and T. Roscilde, Robust spin squeezing from the tower of states of u(1)-symmetric spin Hamiltonians, Phys. Rev. A 105, 022625 (2022).
  29. F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Atomic coherent states in quantum optics, Phys. Rev. A 6, 2211 (1972).
  30. R. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
  31. L. Biedenharn and J. Louck, Encyclopedia of Mathematics and Its Applications: Angular Momentum in Quantum Physics, edited by G.-C. Rota (Addison-Wesley, Reading, MA, 1981), 2nd ed., Vol. 8.
  32. I. V. Protopopov, W. W. Ho, and D. A. Abanin, Effect of SU (2) symmetry on many-body localization and thermalization, Phys. Rev. B 96, 041122 (2017).
  33. N. Debergh and F. Stancu, On the exact solutions of the Lipkin-Meshkov-Glick model, J. Phys. A: Math. Gen. 34, 3265 (2001).
  34. H. Morita, H. Ohnishi, J. da Providência, and S. Nishiyama, Exact solutions for the LMG model Hamiltonian based on the Bethe ansatz, Nucl. Phys. B 737, 337 (2006).
  35. A. B. Klimov and J. L. Romero, A generalized Wigner function for quantum systems with the SU (2) dynamical symmetry group, J. Phys. A: Math. Theor. 41, 055303 (2008).
  36. A. B. Klimov, J. L. Romero, and H. de Guise, Generalized SU (2) covariant Wigner functions and some of their applications, J. Phys. A: Math. Theor. 50, 323001 (2017).
  37. A. Lerose, B. Žunkovič, J. Marino, A. Gambassi, and A. Silva, Impact of nonequilibrium fluctuations on prethermal dynamical phase transitions in long-range interacting spin chains, Phys. Rev. B 99, 045128 (2019).
  38. K. Chinni, P. M. Poggi, and I. H. Deutsch, Effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators, Phys. Rev. Res. 3, 033145 (2021).
  39. Z. Li, A. Delmonte, X. Turkeshi, and R. Fazio, Monitored long-range interacting systems: Spin-wave theory for quantum trajectories, Nat. Commun. 16, 4329 (2025).
  40. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
  41. J. Schachenmayer, A. Pikovski, and A. M. Rey, Many-body quantum spin dynamics with Monte Carlo trajectories on a discrete phase space, Phys. Rev. X 5, 011022 (2015).
  42. J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, Unifying time evolution and optimization with matrix product states, Phys. Rev. B 94, 165116 (2016).
  43. W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Realizing spin squeezing with Rydberg interactions in an optical clock, Nature (London) 621, 734 (2023).
  44. G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mezzacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Scalable spin squeezing in a dipolar Rydberg atom array, Nature (London) 621, 728 (2023).

Outline

Information

Phys. Rev. Research 7, 043056– Published 15 October, 2025
  • Received 14 May 2025
  • Accepted 16 September 2025
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