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  • Letter
  • Open Access

Singular value decomposition and its blind spot for quantum chaos in non-Hermitian Sachdev-Ye-Kitaev models

Matteo Baggioli1,2,3, Kyoung-Bum Huh2, Hyun-Sik Jeong4, Xuhao Jiang2,5,6, Keun-Young Kim7,8, and Juan F. Pedraza4

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Phys. Rev. D 111, L101904 – Published 21 May, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L101904

Abstract

The study of chaos and complexity in non-Hermitian quantum systems poses significant challenges due to the emergence of complex eigenvalues in their spectra. Recently, the singular value decomposition (SVD) method was proposed to address these challenges. In this work, we identify two critical shortcomings of the SVD approach when analyzing Krylov complexity and spectral statistics in non-Hermitian settings. First, we show that SVD fails to reproduce conventional eigenvalue statistics in the Hermitian limit for systems with nonpositive definite spectra, as exemplified by a variant of the Sachdev-Ye-Kitaev (SYK) model. Second, and more fundamentally, Krylov complexity and spectral statistics derived via SVD cannot distinguish chaotic from integrable non-Hermitian dynamics, leading to results that conflict with complex spacing ratio analysis. Our findings reveal that SVD is inadequate for probing quantum chaos in non-Hermitian systems, and we advocate employing more robust methods, such as the bi-Lanczos algorithm, for future research in this direction.

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References (55)

  1. A. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction (Springer, Berlin Heidelberg, 2012).
  2. R. Fazio, J. Keeling, L. Mazza, and M. Schirò, arXiv:2409.10300.
  3. C. M. Bender, Rep. Prog. Phys. 70, 947 (2007).
  4. O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
  5. R. Grobe, F. Haake, and H.-J. Sommers, Phys. Rev. Lett. 61, 1899 (1988).
  6. R. Hamazaki, K. Kawabata, N. Kura, and M. Ueda, Phys. Rev. Res. 2, 023286 (2020).
  7. L. Sá, P. Ribeiro, and T. Prosen, Phys. Rev. X 10, 021019 (2020).
  8. J. Ginibre, J. Math. Phys. (N.Y.) 6, 440 (1965).
  9. G. Akemann, Phys. Rev. Lett. 123, 254101 (2019).
  10. Y. V. Fyodorov, Phys. Rev. Lett. 79, 557 (1997).
  11. J. Li, T. Prosen, and A. Chan, Phys. Rev. Lett. 127, 170602 (2021).
  12. J. Li, S. Yan, T. Prosen, and A. Chan, arXiv:2405.01641.
  13. K. Kawabata, Z. Xiao, T. Ohtsuki, and R. Shindou, PRX Quantum 4, 040312 (2023).
  14. F. Roccati, F. Balducci, R. Shir, and A. Chenu, Phys. Rev. B 109, L140201 (2024).
  15. S. Hamanaka and K. Kawabata, Phys. Rev. B 111, 035144 (2025).
  16. S. H. Tekur, Phys. Rev. B 110, L241410 (2024).
  17. P. Nandy, T. Pathak, and M. Tezuka, Phys. Rev. B 111, L060201 (2025).
  18. P. Nandy, Phys. Rev. B 111, 064203 (2025).
  19. A. M. García-García and V. Godet, Phys. Rev. D 103, 046014 (2021).
  20. K. Su, P. Zhang, and H. Zhai, J. High Energy Phys. 06 (2020) 156.
  21. C. Liu, P. Zhang, and X. Chen, SciPost Phys. 10, 048 (2021).
  22. A. M. García-García, Y. Jia, D. Rosa, and J. J. M. Verbaarschot, Phys. Rev. Lett. 128, 081601 (2022).
  23. P. Zhang, S.-K. Jian, C. Liu, and X. Chen, Quantum 5, 579 (2021).
  24. A. M. García-García, L. Sá, and J. J. M. Verbaarschot, Phys. Rev. X 12, 021040 (2022).
  25. A. M. García-García, Y. Jia, D. Rosa, and J. J. M. Verbaarschot, Phys. Rev. D 105, 126027 (2022).
  26. G. Cipolloni and J. Kudler-Flam, Phys. Rev. Lett. 130, 010401 (2023).
  27. M. V. Berry and M. Tabor, Proc. R. Soc. A 356, 375 (1977).
  28. M. L. Mehta, Random Matrices, 3rd ed. (Academic Press, London, 2004).
  29. R. Grobe, Phys. Rev. Lett. 62, 2893 (1989).
  30. Y. Y. Atas, Phys. Rev. Lett. 110, 084101 (2013).
  31. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, England, 2012).
  32. M. Allard and M. Kieburg, arXiv:2403.19157.
  33. J. Feinberg and A. Zee, Nucl. Phys. B504, 579 (1997).
  34. J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, J. High Energy Phys. 05 (2017) 118; 09 (2018) 002(E).
  35. V. Balasubramanian, P. Caputa, J. M. Magan, and Q. Wu, Phys. Rev. D 106, 046007 (2022).
  36. V. Balasubramanian, J. M. Magan, and Q. Wu, Phys. Rev. E 111, 014218 (2025).
  37. P. Caputa, H.-S. Jeong, S. Liu, J. F. Pedraza, and L.-C. Qu, J. High Energy Phys. 05 (2024) 337.
  38. B. Bhattacharjee and P. Nandy, Phys. Rev. B 111, L060202 (2025).
  39. H.-S. Jeong, A. Kundu, and J. F. Pedraza, arXiv:2412.12301.
  40. J. Erdmenger, S.-K. Jian, and Z.-Y. Xian, J. High Energy Phys. 08 (2023) 176.
  41. S. Chapman, S. Demulder, D. A. Galante, S. U. Sheorey, and O. Shoval, Phys. Rev. B 111, 035141 (2025).
  42. M. Baggioli, K.-B. Huh, H.-S. Jeong, K.-Y. Kim, and J. F. Pedraza, Phys. Rev. Res. 7, 023028 (2025).
  43. K.-B. Huh, H.-S. Jeong, L. A. Pando Zayas, and J. F. Pedraza, arXiv:2412.04963.
  44. K.-B. Huh, H.-S. Jeong, and J. F. Pedraza, J. High Energy Phys. 05 (2024) 137.
  45. C. Lanczos, J. Res. Natl. Bur. Stand. B 45, 255 (1950).
  46. V. S. Viswanath and G. Müller, The Recursion Method: Application to Many-Body Dynamics (Springer, Berlin, Heidelberg, Germany, 1994).
  47. H. A. Camargo, K.-B. Huh, V. Jahnke, H.-S. Jeong, K.-Y. Kim, and M. Nishida, J. High Energy Phys. 08 (2024) 241.
  48. E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, J. High Energy Phys. 06 (2021) 062.
  49. E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, J. High Energy Phys. 07 (2022) 151.
  50. M. Prasad, S. H. Tekur, B. K. Agarwalla, and M. Kulkarni, Phys. Rev. B 111, L161408 (2025).
  51. P. Nandy, A. S. Matsoukas-Roubeas, P. Martínez-Azcona, A. Dymarsky, and A. del Campo, arXiv:2405.09628.
  52. A. Bhattacharya, R. N. Das, B. Dey, and J. Erdmenger, J. High Energy Phys. 03 (2024) 179.
  53. A. Bhattacharyya, S. S. Haque, G. Jafari, J. Murugan, and D. Rapotu, J. High Energy Phys. 10 (2023) 157.
  54. Y. Zhou, W. Xia, L. Li, and W. Li, arXiv:2501.15982.
  55. M. Baggioli, K.-B. Huh, H.-S. Jeong, X. Jiang, K.-Y. Kim, and J. F. Pedraza, Krylov Complexity in Non-Hermitian Sachdev-Ye-Kitaev Models (to be published).

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Phys. Rev. D 111, L101904– Published 21 May, 2025
  • Received 24 March 2025
  • Accepted 2 May 2025
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