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Scrambling transition in free fermion systems induced by a single impurity

Qucheng Gao1, Tianci Zhou2, Pengfei Zhang3,4,*, and Xiao Chen1,†

  • 1Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
  • 2Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
  • 3Department of Physics, Fudan University, Shanghai, 200438, China
  • 4Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China

  • *Contact author: PengfeiZhang.physics@gmail.com
  • †Contact author: chenaad@bc.edu
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Phys. Rev. B 110, 235110 – Published 3 December, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.235110

Abstract

In quantum many-body systems, interactions play a crucial role in the emergence of information scrambling. When particles interact throughout the system, the entanglement between them can lead to a rapid and chaotic spreading of quantum information, typically probed by the growth in operator size in the Heisenberg picture. In this study, we explore whether the operator undergoes scrambling when particles interact solely through a single impurity in generic spatial dimensions, focusing on fermion systems with spatial and temporal random hoppings. By connecting the dynamics of the operator to the symmetric exclusion process with a source term, we demonstrate the presence of an escape-to-scrambling transition when tuning the interaction strength for fermions in three dimensions. As a comparison, systems in lower dimensions are proven to scramble at arbitrarily weak interactions unless the hopping becomes sufficiently long-ranged. Our predictions are validated using both a Brownian circuit with a single Majorana fermion per site and a solvable Brownian SYK model with a large local Hilbert space dimension. This suggests the universality of the theoretical picture for free fermion systems with spatial and temporal randomness.

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References (64)

  1. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  2. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  3. Y. Sekino and L. Susskind, Fast scramblers, J. High Energy Phys. 10 (2008) 065.
  4. P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, J. High Energy Phys. 09 (2007) 120.
  5. S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 03 (2014) 067.
  6. S. H. Shenker and D. Stanford, Stringy effects in scrambling, J. High Energy Phys. 05 (2015) 132.
  7. D. A. Roberts, D. Stanford, and L. Susskind, Localized shocks, J. High Energy Phys. 03 (2015) 051.
  8. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 106.
  9. D. A. Roberts, D. Stanford, and A. Streicher, Operator growth in the SYK model, J. High Energy Phys. 06 (2018) 122.
  10. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech.: Theory Exp. (2005) P04010 .
  11. A. Nahum, S. Vijay, and J. Haah, Operator spreading in random unitary circuits, Phys. Rev. X 8, 021014 (2018).
  12. N. Hunter-Jones, Operator growth in random quantum circuits with symmetry, arXiv:1812.08219.
  13. C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws, Phys. Rev. X 8, 021013 (2018).
  14. V. Khemani, A. Vishwanath, and D. A. Huse, Operator spreading and the emergence of dissipation in unitary dynamics with conservation laws, Phys. Rev. X 8, 031057 (2018).
  15. X.-L. Qi and A. Streicher, Quantum epidemiology: Operator growth, thermal effects, and SYK, J. High Energy Phys. 08 (2019) 012.
  16. B. C. Dias, M. Haque, P. Ribeiro, and P. McClarty, Diffusive operator spreading for random unitary free fermion circuits, arXiv:2102.09846.
  17. Y. Wu, P. Zhang, and H. Zhai, Scrambling ability of quantum neural network architectures, Phys. Rev. Res. 3, L032057 (2021).
  18. X.-L. Qi, E. J. Davis, A. Periwal, and M. Schleier-Smith, Measuring operator size growth in quantum quench experiments, arXiv:1906.00524.
  19. T. Zhou and B. Swingle, Operator growth from global out-of-time-order correlators, Nat. Commun. 14, 3411 (2021).
  20. S. Omanakuttan, K. Chinni, P. D. Blocher, and P. M. Poggi, Scrambling and quantum chaos indicators from long-time properties of operator distributions, Phys. Rev. A 107, 032418 (2023).
  21. P. Zhang and Y. Gu, Operator size distribution in large N quantum mechanics of Majorana fermions, J. High Energy Phys. 10 (2023) 018.
  22. Z. Liu and P. Zhang, Signature of scramblon effective field theory in random spin models, Phys. Rev. Lett. 132, 060201 (2024).
  23. A. Lucas, Operator size at finite temperature and planckian bounds on quantum dynamics, Phys. Rev. Lett. 122, 216601 (2019).
  24. A. Lucas and A. Osborne, Operator growth bounds in a cartoon matrix model, J. Math. Phys. 61, 122301 (2020).
  25. X. Chen, Y. Gu, and A. Lucas, Many-body quantum dynamics slows down at low density, SciPost Phys. 9, 071 (2020).
  26. C.-F. Chen and A. Lucas, Operator growth bounds from graph theory, Commun. Math. Phys. 385, 1273 (2021).
  27. C. Yin and A. Lucas, Quantum operator growth bounds for kicked tops and semiclassical spin chains, Phys. Rev. A 103, 042414 (2021).
  28. S. Xu and B. Swingle, Locality, quantum fluctuations, and scrambling, Phys. Rev. X 9, 031048 (2019).
  29. T. Zhou and X. Chen, Operator dynamics in a Brownian quantum circuit, Phys. Rev. E 99, 052212 (2019).
  30. X. Chen and T. Zhou, Quantum chaos dynamics in long-range power law interaction systems, Phys. Rev. B 100, 064305 (2019).
  31. T. Zhou, S. Xu, X. Chen, A. Guo, and B. Swingle, Operator Lévy flight: Light cones in chaotic long-range interacting systems, Phys. Rev. Lett. 124, 180601 (2020).
  32. N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the fast scrambling conjecture, J. High Energy Phys. 04 (2013) 022.
  33. Q. Gao, P. Zhang, and X. Chen, Information scrambling in free fermion systems with a sole interaction, Phys. Rev. B 110, 035137 (2024).
  34. R. A. Blythe and M. R. Evans, Nonequilibrium steady states of matrix-product form: a solver's guide, J. Phys. A: Math. Theor. 40, R333 (2007).
  35. G. T. Landi, D. Poletti, and G. Schaller, Nonequilibrium boundary-driven quantum systems: Models, methods, and properties, Rev. Mod. Phys. 94, 045006 (2022).
  36. B. Dóra, M. A. Werner, and C. P. Moca, Information scrambling at an impurity quantum critical point, Phys. Rev. B 96, 155116 (2017).
  37. S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993).
  38. A. Kitaev, A simple model of quantum holography (2015).
  39. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016).
  40. A. Kitaev and S. J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, J. High Energy Phys. 05 (2018) 183.
  41. Y. Gu, X.-L. Qi, and D. Stanford, Local criticality, diffusion and chaos in generalized sachdev-ye-kitaev models, J. High Energy Phys. 05 (2017) 125.
  42. P. Saad, S. H. Shenker, and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840.
  43. C. Sünderhauf, L. Piroli, X.-L. Qi, N. Schuch, and J. I. Cirac, Quantum chaos in the Brownian SYK model with large finite N: OTOCs and tripartite information, J. High Energy Phys. 11 (2019) 038.
  44. D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids, Rev. Mod. Phys. 94, 035004 (2022).
  45. T. M. Liggett and T. M. Liggett, Interacting Particle Systems (Springer, Berlin, 1985), Vol. 2.
  46. F. Spitzer, Interaction of markov processes, in Random Walks, Brownian Motion, and Interacting Particle Systems: A Festschrift in Honor of Frank Spitzer (Springer, Berlin, 1991), pp. 66–110.
  47. R. Lyons, Random walks and percolation on trees, Ann. Probab. 18, 931 (1990).
  48. G. Pólya, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz, Math. Ann. 84, 149 (1921).
  49. E. W. Weisstein, Pólya's Random Walk Constants, https://mathworld.wolfram.com/PolyasRandomWalkConstants.html.
  50. P. Zhang, Y. Gu, and A. Kitaev, An obstacle to sub-AdS holography for SYK-like models, J. High Energy Phys. 03 (2021) 094.
  51. A. J. Guttmann, Lattice Green's functions in all dimensions, J. Phys. A 43, 305205 (2010).
  52. P. Zhang, C. Liu, S.-K. Jian, and X. Chen, Universal entanglement transitions of free fermions with long-range non-unitary dynamics, Quantum 6, 723 (2022).
  53. S. Sahu, S.-K. Jian, G. Bentsen, and B. Swingle, Entanglement phases in large-N hybrid Brownian circuits with long-range couplings, Phys. Rev. B 106, 224305 (2022).
  54. M. Block, Y. Bao, S. Choi, E. Altman, and N. Y. Yao, Measurement-induced transition in long-range interacting quantum circuits, Phys. Rev. Lett. 128, 010604 (2022).
  55. T. Müller, S. Diehl, and M. Buchhold, Measurement-induced dark state phase transitions in long-ranged fermion systems, Phys. Rev. Lett. 128, 010605 (2022).
  56. T. Minato, K. Sugimoto, T. Kuwahara, and K. Saito, Fate of measurement-induced phase transition in long-range interactions, Phys. Rev. Lett. 128, 010603 (2022).
  57. P. Zhang and Z. Yu, Dynamical transition of operator size growth in quantum systems embedded in an environment, Phys. Rev. Lett. 130, 250401 (2023).
  58. Z. Weinstein, S. P. Kelly, J. Marino, and E. Altman, Scrambling transition in a radiative random unitary circuit, Phys. Rev. Lett. 131, 220404 (2023).
  59. D. Gribben, J. Marino, and S. P. Kelly, Markovian to non-markovian phase transition in the operator dynamics of a mobile impurity, SciPost Phys. Core 7, 060 (2024).
  60. P. L. Krapivsky, Symmetric exclusion process with a localized source, Phys. Rev. E 86, 041103 (2012).
  61. P. Krapivsky and D. Stefanovic, Lattice gases with a point source, J. Stat. Mech.: Theory Exp. (2014) P09003.
  62. M. Bauer, P. L. Krapivsky, and K. Mallick, Random walk through a fertile site, Phys. Rev. E 103, 022114 (2021).
  63. P. Krapivsky, K. Mallick, and D. Sels, Free fermions with a localized source, J. Stat. Mech.: Theory Exp. (2019) 113108.
  64. P. Krapivsky, K. Mallick, and D. Sels, Free bosons with a localized source, J. Stat. Mech.: Theory Exp. (2020) 063101.

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Phys. Rev. B 110, 235110– Published 3 December, 2024
  • Received 20 April 2024
  • Revised 16 October 2024
  • Accepted 20 November 2024
Article part of CHORUS
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