- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Timescales of quantum and classical chaotic spin models evolving toward equilibrium

Fausto Borgonovi1,2,*, Felix M. Izrailev3,4, and Lea F. Santos5

  • *Contact author: fausto.borgonovi@unicatt.it
PDF

Phys. Rev. E 111, 044210 – Published 14 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044210

Abstract

We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical relaxation. Numerical simulations, supported by semianalytical analysis, reveal that the relaxation of single-particle energies (global quantity) and on-site magnetization (local observable) occurs on a timescale independent of the system size L. This relaxation process is equally well-described by classical equations of motion and quantum solutions, demonstrating excellent quantum-classical correspondence, provided the system is strongly chaotic. The correspondence persists even for small quantum spin values (S=1), where a semiclassical approximation is not applicable. Conversely, for the participation ratio, which characterizes the initial state spread in the many-body Hilbert space and which lacks a classical analog, the relaxation timescale is system-size dependent.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (47)

  1. S. Goldstein, T. Hara, and H. Tasaki, Time scales in the approach to equilibrium of macroscopic quantum systems, Phys. Rev. Lett. 111, 140401 (2013).
  2. S. Goldstein, T. Hara, and H. Tasaki, Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace, New J. Phys. 17, 045002 (2015).
  3. T. R. de Oliveira, C. Charalambous, D. Jonathan, M. Lewenstein, and A. Riera, Equilibration time scales in closed many-body quantum systems, New J. Phys. 20, 033032 (2018).
  4. G. D. Carvalho, L. F. dos Prazeres, P. S. Correia, and T. R. de Oliveira, Equilibration of isolated systems: Investigating the role of coarse-graining on the initial state magnetization Phys. Lett. A 494, 129276 (2024).
  5. M. Niknam, L. F. Santos, and D. G. Cory, Experimental detection of the correlation Rényi entropy in the central spin model, Phys. Rev. Lett. 127, 080401 (2021).
  6. P. Reimann, Foundation of statistical mechanics under experimentally realistic conditions, Phys. Rev. Lett. 101, 190403 (2008).
  7. P. Reimann, Typical fast thermalization processes in closed many-body systems, Nat. Commun. 7, 10821 (2016).
  8. A. J. Short, Equilibration of quantum systems and subsystems, New J. Phys. 13, 053009 (2011).
  9. A. J. Short and T. C. Farrelly, Quantum equilibration in finite time, New J. Phys. 14, 013063 (2012).
  10. T. Monnai, Generic evaluation of relaxation time for quantum many-body systems: Analysis of the system size dependence, J. Phys. Soc. Jpn. 82, 044006 (2013).
  11. A. S. L. Malabarba, L. P. García-Pintos, N. Linden, T. C. Farrelly, and A. J. Short, Quantum systems equilibrate rapidly for most observables, Phys. Rev. E 90, 012121 (2014).
  12. D. Hetterich, M. Fuchs, and B. Trauzettel, Equilibration in closed quantum systems: Application to spin qubits, Phys. Rev. B 92, 155314 (2015).
  13. C. Gogolin and J. Eisert, Equilibration, thermalization, and the emergence of statistical mechanics in closed quantum systems, Rep. Prog. Phys. 79, 056001 (2016).
  14. L. P. García-Pintos, N. Linden, A. S. L. Malabarba, A. J. Short, and A. Winter, Equilibration time scales of physically relevant observables, Phys. Rev. X 7, 031027 (2017).
  15. M. Schiulaz, E. J. Torres-Herrera, and L. F. Santos, Thouless and relaxation time scales in many-body quantum systems, Phys. Rev. B 99, 174313 (2019).
  16. B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, and M. Žnidarič, Finite-temperature transport in one-dimensional quantum lattice models, Rev. Mod. Phys. 93, 025003 (2021).
  17. A. Dymarsky, Bound on eigenstate thermalization from transport, Phys. Rev. Lett. 128, 190601 (2022).
  18. T. L. M. Lezama, E. J. Torres-Herrera, F. Pérez-Bernal, Y. Bar Lev, and L. F. Santos, Equilibration time in many-body quantum systems, Phys. Rev. B 104, 085117 (2021).
  19. L. Benet, F. Borgonovi, F. M. Izrailev, and L. F. Santos, Quantum-classical correspondence of strongly chaotic many-body spin models, Phys. Rev. B 107, 155143 (2023).
  20. V. Zelevinsky, B. A. Brown, N. Frazier, and M. Horoi, The nuclear shell model as a testing ground for many-body quantum chaos, Phys. Rep. 276, 85 (1996).
  21. F. Borgonovi, F. M. Izrailev, and L. F. Santos, Exponentially fast dynamics of chaotic many-body systems, Phys. Rev. E 99, 010101(R) (2019).
  22. F. Borgonovi, F. M. Izrailev, and L. F. Santos, Timescales in the quench dynamics of many-body quantum systems: Participation ratio versus out-of-time ordered correlator, Phys. Rev. E 99, 052143 (2019).
  23. J. Rammensee, J. D. Urbina, and K. Richter, Many-body quantum interference and the saturation of out-of-time-order correlators, Phys. Rev. Lett. 121, 124101 (2018).
  24. Q. Hummel, B. Geiger, J. D. Urbina, and K. Richter, Reversible quantum information spreading in many-body systems near criticality, Phys. Rev. Lett. 123, 160401 (2019).
  25. M. Akila, D. Waltner, B. Gutkin, P. Braun, and T. Guhr, Semiclassical identification of periodic orbits in a quantum many-body system, Phys. Rev. Lett. 118, 164101 (2017).
  26. M. Akila, B. Gutkin, P. Braun, D. Waltner, and T. Guhr, Semiclassical prediction of large spectral fluctuations in interacting kicked spin chains, Ann. Phys. 389, 250 (2018).
  27. D. Schubert, J. Richter, F. Jin, K. Michielsen, H. D. Raedt, and R. Steinigeweg, Quantum versus classical dynamics in spin models: Chains, ladders, and square lattices, Phys. Rev. B 104, 054415 (2021).
  28. L. Correale, A. Polkovnikov, M. Schirò, and A. Silva, Probing chaos in the spherical p-spin glass model, SciPost Phys. 15, 190 (2023).
  29. F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, Quantum chaos and thermalization in isolated systems of interacting particles, Phys. Rep. 626, 1 (2016).
  30. 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) .
  31. P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature (London) 511, 202 (2014).
  32. 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).
  33. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys. 12, 907 (2016).
  34. L. Feng, O. Katz, C. Haack, M. Maghrebi, A. V. Gorshkov, Z. Gong, M. Cetina, and C. Monroe, Continuous symmetry breaking in a trapped-ion spin chain, Nature (London) 623, 713 (2023).
  35. D. Zhang, H. T. Quan, and B. Wu, Ergodicity and mixing in quantum dynamics, Phys. Rev. E 94, 022150 (2016).
  36. G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, Stochastic behavior of a quantum pendulum under a periodic perturbation, Lect. Notes in Phys. 93, 334 (1979).
  37. B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, Dynamical stochasticity in classical and quantum mechanics, Sov. Sci. Rev. C 2, 209 (1981).
  38. J. Steinberg and B. Swingle, Thermalization and chaos in QED3, Phys. Rev. D99, 076007 (2019).
  39. M. Malishava and S. Flach, Thermalization dynamics of macroscopic weakly nonintegrable maps, Chaos 32, 063113 (2022).
  40. M. Malishava and S. Flach, Lyapunov spectrum scaling for classical many-body dynamics close to integrability, Phys. Rev. Lett. 128, 134102 (2022).
  41. Z. Wang, Y. Wang, and B. Wu, Quantum chaos and physical distance between quantum states, Phys. Rev. E 103, 042209 (2021).
  42. T. Bilitewski, S. Bhattacharjee, and R. Moessner, Classical many-body chaos with and without quasiparticles, Phys. Rev. B 103, 174302 (2021).
  43. L. F. Santos, F. Borgonovi, and G. L. Celardo, Cooperative shielding in many-body systems with long-range interaction, Phys. Rev. Lett. 116, 250402 (2016).
  44. F. Lillo and R. N. Mantegna, Anomalous spreading of power-law quantum wave packets, Phys. Rev. Lett. 84, 1061 (2000).
  45. S. Miccichè, Modeling long-range memory with stationary Markovian processes, Phys. Rev. E 79, 031116 (2009).
  46. S. Miccichè, A. Buchleitner, F. Lillo, R. N. Mantegna, T. Paul, and S. Wimberger, Scale-free relaxation of a wave packet in a quantum well with power-law tails, New J. Phys. 15, 033033 (2013).
  47. F. Borgonovi, G. Celardo, F. M. Izrailev, and G. Casati, A semiquantal approach to finite systems of interacting particles, Phys. Rev. Lett. 88, 054101 (2002).

Outline

Information

Phys. Rev. E 111, 044210– Published 14 April, 2025
  • Received 19 November 2024
  • Revised 17 February 2025
  • Accepted 21 March 2025
Article part of CHORUS
Crossmark - Check for updates button

©2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation