Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
194 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Scrambling Transition in Free Fermion Systems Induced by a Single Impurity (2403.03457v2)

Published 6 Mar 2024 in quant-ph and cond-mat.stat-mech

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.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  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, Journal of High Energy Physics 2008, 065 (2008).
  4. P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, Journal of High Energy Physics 2007, 120 (2007).
  5. S. H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03, 067, arXiv:1306.0622 [hep-th] .
  6. S. H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05, 132, arXiv:1412.6087 [hep-th] .
  7. D. A. Roberts, D. Stanford, and L. Susskind, Localized shocks, JHEP 03, 051, arXiv:1409.8180 [hep-th] .
  8. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, JHEP 08, 106, arXiv:1503.01409 [hep-th] .
  9. D. A. Roberts, D. Stanford, and A. Streicher, Operator growth in the SYK model, JHEP 06, 122, arXiv:1802.02633 [hep-th] .
  10. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, Journal of Statistical Mechanics: Theory and Experiment 2005, P04010 (2005).
  11. A. Nahum, S. Vijay, and J. Haah, Operator Spreading in Random Unitary Circuits, Phys. Rev. X 8, 021014 (2018), arXiv:1705.08975 [cond-mat.str-el] .
  12. N. Hunter-Jones, Operator growth in random quantum circuits with symmetry,   (2018), arXiv:1812.08219 [quant-ph] .
  13. 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), arXiv:1710.09835 [cond-mat.stat-mech] .
  14. Y. Wu, P. Zhang, and H. Zhai, Scrambling ability of quantum neural network architectures, Phys. Rev. Research 3, L032057 (2021).
  15. T. Zhou and B. Swingle, Operator Growth from Global Out-of-time-order Correlators,   (2021), arXiv:2112.01562 [quant-ph] .
  16. P. Zhang and Y. Gu, Operator size distribution in large N quantum mechanics of Majorana fermions, JHEP 10, 018, arXiv:2212.04358 [cond-mat.str-el] .
  17. Z. Liu and P. Zhang, Signature of Scramblon Effective Field Theory in Random Spin Models, Phys. Rev. Lett. 132, 060201 (2024), arXiv:2306.05678 [quant-ph] .
  18. A. Lucas, Operator size at finite temperature and planckian bounds on quantum dynamics, Phys. Rev. Lett. 122, 216601 (2019).
  19. A. Lucas and A. Osborne, Operator growth bounds in a cartoon matrix model, J. Math. Phys. 61, 122301 (2020), arXiv:2007.07165 [hep-th] .
  20. X. Chen, Y. Gu, and A. Lucas, Many-body quantum dynamics slows down at low density, SciPost Phys. 9, 071 (2020), arXiv:2007.10352 [quant-ph] .
  21. C.-F. Chen and A. Lucas, Operator Growth Bounds from Graph Theory, Commun. Math. Phys. 385, 1273 (2021), arXiv:1905.03682 [math-ph] .
  22. C. Yin and A. Lucas, Quantum operator growth bounds for kicked tops and semiclassical spin chains, Phys. Rev. A 103, 042414 (2021), arXiv:2010.06592 [cond-mat.str-el] .
  23. T. Zhou and X. Chen, Operator dynamics in a brownian quantum circuit, Phys. Rev. E 99, 052212 (2019).
  24. X. Chen and T. Zhou, Quantum chaos dynamics in long-range power law interaction systems, Physical Review B 100, 10.1103/physrevb.100.064305 (2019).
  25. Q. Gao, P. Zhang, and X. Chen, Information scrambling in free fermion systems with a sole interaction, arXiv preprint arXiv:2310.07043  (2023).
  26. S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70, 3339 (1993), arXiv:cond-mat/9212030 [cond-mat] .
  27. A. Kitaev, A simple model of quantum holography (2015).
  28. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016), arXiv:1604.07818 [hep-th] .
  29. A. Kitaev and S. J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05, 183, arXiv:1711.08467 [hep-th] .
  30. P. Saad, S. H. Shenker, and D. Stanford, A semiclassical ramp in SYK and in gravity,   (2018), arXiv:1806.06840 [hep-th] .
  31. T. M. Liggett and T. M. Liggett, Interacting particle systems, Vol. 2 (Springer, 1985).
  32. R. Lyons, Random walks and percolation on trees, The annals of Probability 18, 931 (1990).
  33. G. Pólya, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz, Mathematische Annalen 84, 149 (1921).
  34. E. W. Weisstein, Pólya’s random walk constants.
  35. P. Zhang, Y. Gu, and A. Kitaev, An obstacle to sub-AdS holography for SYK-like models, JHEP 21, 094, arXiv:2012.01620 [hep-th] .
  36. A. J. Guttmann, Lattice Green’s functions in all dimensions, Journal of Physics A Mathematical General 43, 305205 (2010), arXiv:1004.1435 [math-ph] .
  37. T. Müller, S. Diehl, and M. Buchhold, Measurement-induced dark state phase transitions in long-ranged fermion systems, Phys. Rev. Lett. 128, 010605 (2022).
  38. P. Zhang and Z. Yu, Dynamical transition of operator size growth in quantum systems embedded in an environment, Phys. Rev. Lett. 130, 250401 (2023).

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets