- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Out-of-time ordered correlation functions for the localized f electrons in the Falicov-Kimball model

A. M. Shvaika

J. K. Freericks

PDF

Phys. Rev. B 113, 035114 – Published 6 January, 2026

DOI: https://doi.org/10.1103/cpkv-w6m1

Abstract

We provide an exact evaluation of the out-of-time correlation (OTOC) functions for the localized f-particle states in the Falicov-Kimball model within dynamical mean-field theory. Different regimes of quantum chaos and quantum scrambling are distinguished by the winding numbers of the block Toeplitz matrices used in the calculation. The similarities of these fermionic OTOCs and their logarithmic derivatives for time evolution with the OTOCs for quantum spin models with disorder are also discussed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. S. Xu and B. Swingle, Scrambling dynamics and out-of-time-ordered correlators in quantum many-body systems, PRX Quantum 5, 010201 (2024).
  2. I. García-Mata, R. A. Jalabert, and D. A. Wisniacki, Out-of-time-order correlators and quantum chaos, Scholarpedia 18, 55237 (2023).
  3. P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, J. High Energy Phys. 09 (2007) 120.
  4. D. A. Roberts and D. Stanford, Diagnosing chaos using four-point functions in two-dimensional conformal field theory, Phys. Rev. Lett. 115, 131603 (2015).
  5. A. I. Larkin and Yu. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Zh. Eksp. Teor. Fiz. 55, 2262 (1968) [Sov. Phys. JETP 28, 1200 (1969)].
  6. A. Peres, Stability of quantum motion in chaotic and regular systems, Phys. Rev. A 30, 1610 (1984).
  7. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 106.
  8. S. Xu and B. Swingle, Locality, quantum fluctuations, and scrambling, Phys. Rev. X 9, 031048 (2019).
  9. P. D. Bergamasco, G. G. Carlo, and A. M. F. Rivas, Quantum Lyapunov exponent in dissipative systems, Phys. Rev. E 108, 024208 (2023).
  10. P. D. Bergamasco, G. G. Carlo, and A. M. F. Rivas, Spectral truncation of out-of-time-ordered correlators in dissipative systems, Phys. Rev. E 112, 034201 (2025).
  11. C.-J. Lin and O. I. Motrunich, Out-of-time-ordered correlators in a quantum Ising chain, Phys. Rev. B 97, 144304 (2018).
  12. J. Riddell and E. S. Sørensen, Out-of-time ordered correlators and entanglement growth in the random-field XX spin chain, Phys. Rev. B 99, 054205 (2019).
  13. S. Xu and B. Swingle, Accessing scrambling using matrix product operators, Nat. Phys. 16, 199 (2020).
  14. P. V. Buividovich, Quantum chaos in supersymmetric quantum mechanics: An exact diagonalization study, Phys. Rev. D 106, 046001 (2022).
  15. J. Kim, X. Cao, and E. Altman, Scrambling versus relaxation in Fermi and non-Fermi liquids, Phys. Rev. B 102, 085134 (2020).
  16. L. M. Falicov and J. C. Kimball, Simple model for semiconductor-metal transitions: SmB6 and transition-metal oxides, Phys. Rev. Lett. 22, 997 (1969).
  17. U. Brandt and R. Schmidt, Exact results for the distribution of the f-level ground state occupation in the spinless Falicov-Kimball model, Z. Phys. B 63, 45 (1986).
  18. T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long range order, Physica A 138, 320 (1986).
  19. T. Kennedy, Some rigorous results on the ground states of the Falicov-Kimball model, Rev. Math. Phys. 06, 901 (1994).
  20. C. Gruber, N. Macris, A. Messager, and D. Ueltschi, Ground states and flux configurations of the two-dimensional Falicov-Kimball model, J. Stat. Phys. 86, 57 (1997).
  21. N. Datta, R. Fernández, and J. Fröhlich, Effective Hamiltonians and phase diagrams for tight-binding models, J. Stat. Phys. 96, 545 (1999).
  22. J. Wojtkiewicz and R. Lemański, Ground states of the Falicov-Kimball model with correlated hopping, Phys. Rev. B 64, 233103 (2001).
  23. U. Brandt and C. Mielsch, Thermodynamics and correlation functions of the Falicov-Kimball model in large dimensions, Z. Phys. B 75, 365 (1989).
  24. J. K. Freericks and V. Zlatić, Exact dynamical mean-field theory of the Falicov-Kimball model, Rev. Mod. Phys. 75, 1333 (2003).
  25. W. Metzner and D. Vollhardt, Correlated lattice fermions in d=∞ dimensions, Phys. Rev. Lett. 62, 324 (1989).
  26. W. Metzner, Linked-cluster expansion around the atomic limit of the Hubbard model, Phys. Rev. B 43, 8549 (1991).
  27. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
  28. U. Brandt and M. P. Urbanek, The f-electron spectrum of the spinless Falicov-Kimball model in large dimensions, Z. Phys. B 89, 297 (1992).
  29. J. K. Freericks, V. M. Turkowski, and V. Zlatić, F-electron spectral function of the Falicov-Kimball model in infinite dimensions: The half-filled case, Phys. Rev. B 71, 115111 (2005).
  30. A. M. Shvaika and J. K. Freericks, F-electron spectral function of the Falicov-Kimball model and the Wiener-Hopf sum equation approach, Condens. Matter Phys. 11, 425 (2008).
  31. N. Tsuji, P. Werner, and M. Ueda, Exact out-of-time-ordered correlation functions for an interacting lattice fermion model, Phys. Rev. A 95, 011601(R) (2017).
  32. V. Zlatić, J. K. Freericks, R. Lemański, and G. Czycholl, Exact solution of the multicomponent Falicov-Kimball model in infinite dimensions, Philos. Mag. B 81, 1443 (2001).
  33. N. Pakhira, A. M. Shvaika, and J. K. Freericks, X-ray photoemission spectroscopy in the Falicov-Kimball model, Phys. Rev. B 99, 125137 (2019).
  34. P. Nozières and C. T. De Dominicis, Singularities in the x-ray absorption and emission of metals. III. One-body theory exact solution, Phys. Rev. 178, 1097 (1969).
  35. N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of Functions Theory and Their Applications to Mathematical Physics (Springer Netherlands, Dordrecht, 1977).
  36. H. Widom, Asymptotic behavior of block Toeplitz matrices and determinants. II, Adv. Math. 21, 1 (1976).
  37. Despite the chaos bound of [7, 8] is applicable for the short timescale, we compare the decay rate with this temperature bound to elucidate thermal effects in relaxation.
  38. Now, DOS is defined by the real part of OTOC because (5.1) omits factor “−i” in contrast to the one-particle Green's function (2.12).
  39. N. Yunger Halpern, Jarzynski-like equality for the out-of-time-ordered correlator, Phys. Rev. A 95, 012120 (2017).
  40. N. Yunger Halpern, B. Swingle, and J. Dressel, Quasiprobability behind the out-of-time-ordered correlator, Phys. Rev. A 97, 042105 (2018).
  41. J. R. González Alonso, N. Yunger Halpern, and J. Dressel, Out-of-time-ordered-correlator quasiprobabilities robustly witness scrambling, Phys. Rev. Lett. 122, 040404 (2019).
  42. A. Levy and M. Lostaglio, Quasiprobability distribution for heat fluctuations in the quantum regime, PRX Quantum 1, 010309 (2020).
  43. S. Gherardini and G. De Chiara, Quasiprobabilities in quantum thermodynamics and many-body systems, PRX Quantum 5, 030201 (2024).
  44. P. W. Anderson, Infrared catastrophe in Fermi gases with local scattering potentials, Phys. Rev. Lett. 18, 1049 (1967).
  45. A. Shvaika and J. Freericks, OTOC functions for the localized f electrons in the Falicov-Kimball model (2025), doi: 10.5281/zenodo.17041485.

Outline

Information

Phys. Rev. B 113, 035114– Published 6 January, 2026
  • Received 2 September 2025
  • Revised 14 December 2025
  • Accepted 16 December 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