Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 43 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 21 tok/s Pro
GPT-5 High 20 tok/s Pro
GPT-4o 95 tok/s Pro
Kimi K2 180 tok/s Pro
GPT OSS 120B 443 tok/s Pro
Claude Sonnet 4.5 32 tok/s Pro
2000 character limit reached

Integrability as an attractor of adiabatic flows (2308.09745v4)

Published 18 Aug 2023 in cond-mat.stat-mech and quant-ph

Abstract: The interplay between quantum chaos and integrability has been extensively studied in the past decades. We approach this topic from the point of view of geometry encoded in the quantum geometric tensor, which describes the complexity of adiabatic transformations. In particular, we consider two generic models of spin chains that are parameterized by two independent couplings. In one, the integrability breaking perturbation is global while, in the other, integrability is broken only at the boundary. In both cases, the shortest paths in the coupling space lead towards integrable regions and we argue that this behavior is generic. These regions thus act as attractors of adiabatic flows similar to river basins in nature. Physically, the directions towards integrable regions are characterized by faster relaxation dynamics than those parallel to integrability, and the anisotropy between them diverges in the thermodynamic limit as the system approaches the integrable point. We also provide evidence that the transition from integrable to chaotic behavior is universal for both models, similar to continuous phase transitions, and that the model with local integrability breaking quickly becomes chaotic but avoids ergodicity.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  1. M. Berry, Physica Scripta 40, 335 (1989).
  2. F. Haake, Quantum signatures of chaos, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer (Springer US, Boston, MA, 1991) pp. 583–595.
  3. H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, 1999).
  4. T. Guhr, A. Müller–Groeling, and H. A. Weidenmüller, Physics Reports 299, 189 (1998).
  5. M. Srednicki, Journal of Physics A: Mathematical and General 32, 1163 (1999).
  6. J. M. Deutsch, Reports on Progress in Physics 81, 082001 (2018).
  7. M. V. Berry and M. Tabor, Proceedings of the Royal Society of London Series A 356, 375 (1977).
  8. J. Berges, S. Borsányi, and C. Wetterich, Phys. Rev. Lett. 93, 142002 (2004).
  9. M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008).
  10. V. A. Yurovsky and M. Olshanii, Phys. Rev. Lett. 106, 025303 (2011).
  11. J. Durnin, M. J. Bhaseen, and B. Doyon, Phys. Rev. Lett. 127, 130601 (2021).
  12. V. Gurarie, Field theory and the phenomenon of turbulence (1995), arXiv:hep-th/9501021 [hep-th] .
  13. Z. Lenarčič, F. Lange, and A. Rosch, Phys. Rev. B 97, 024302 (2018).
  14. V. B. Bulchandani, D. A. Huse, and S. Gopalakrishnan, Phys. Rev. B 105, 214308 (2022).
  15. F. M. Surace and O. Motrunich, Phys. Rev. Res. 5, 043019 (2023).
  16. P. Zanardi and N. Paunković, Phys. Rev. E 74, 031123 (2006).
  17. L. Campos Venuti and P. Zanardi, Phys. Rev. Lett. 99, 095701 (2007).
  18. M. Kolodrubetz, V. Gritsev, and A. Polkovnikov, Phys. Rev. B 88, 064304 (2013).
  19. D. Sels and A. Polkovnikov, Phys. Rev. E 104, 054105 (2021).
  20. Y. Zhang, L. Vidmar, and M. Rigol, Phys. Rev. E 106, 014132 (2022).
  21. J. Provost and G. Vallee, Commun. Math. Phys. 76, 289 (1980).
  22. C. W. Helstrom, Quantum Detection and Estimation Theory, ISSN (Elsevier Science, 1976).
  23. M. Bukov, D. Sels, and A. Polkovnikov, Phys. Rev. X 9, 011034 (2019).
  24. S. Peotta, K.-E. Huhtinen, and P. Törmä, Quantum geometry in superfluidity and superconductivity (2023), arXiv:2308.08248 [cond-mat.quant-gas] .
  25. In this paper, we are only interested in its real part also referred to as Fubini-Study metric tensor.
  26. For all subsequent calculations, we always consider only the central 50%percent5050\%50 % of the eigenstates.
  27. 1/𝒟s1subscript𝒟𝑠1/\mathcal{D}_{s}1 / caligraphic_D start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT is approximately the level spacing of the system.
  28. A. Gubin and L. F. Santos, Am. J. Phys 80, 246 (2012).
  29. H. Kim, T. N. Ikeda, and D. A. Huse, Phys. Rev. E 90, 052105 (2014).
  30. M. Brenes, J. Goold, and M. Rigol, Phys. Rev. B 102, 075127 (2020).
  31. L. Chierchia and J. N. Mather, Scholarpedia 5, 2123 (2010), revision #91405.
  32. D. Sels and A. Polkovnikov, Proceedings of the National Academy of Sciences 114, E3909 (2017).
  33. S. J. Garratt, S. Roy, and J. T. Chalker, Phys. Rev. B 104, 184203 (2021).
  34. S. J. Garratt and S. Roy, Phys. Rev. B 106, 054309 (2022).
  35. Note that 1/μ21superscript𝜇21/\mu^{2}1 / italic_μ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT scaling can be also explained if Φ𝔫⁢(ω)subscriptΦ𝔫𝜔\Phi_{\mathfrak{n}}(\omega)roman_Φ start_POSTSUBSCRIPT fraktur_n end_POSTSUBSCRIPT ( italic_ω ) decays faster than 1/ω1𝜔1/\omega1 / italic_ω but then there must exist a low frequency cutoff below which the spectral function must saturate [18].
  36. M. Kolodrubetz, E. Katz, and A. Polkovnikov, Phys. Rev. B 91, 054306 (2015).
  37. P. Weinberg and M. Bukov, SciPost Phys. 2, 003 (2017).
  38. P. Weinberg and M. Bukov, SciPost Phys. 7, 020 (2019).
Citations (2)
View on Semantic Scholar

Summary

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up