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  • Open Access

Testing dynamical stabilization of complex Langevin simulations of QCD

Michael Westh Hansen* and Dénes Sexty

  • *Contact author: michael.hansen@uni-graz.at

Phys. Rev. D 111, 054508 – Published 14 March, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.054508

Abstract

We study complex Langevin simulations of a toy model as well as QCD, supplemented with a dynamical stabilization (DS) term, which was proposed to regularize the complexified process at lower temperatures. We compare the results to reweighting from zero chemical potential to measure the bias that the inclusion of the stabilization term causes, depending on its strength. At high temperatures the stabilization term is not needed. At low temperatures (below deconfinement transition) the DS term has a beneficial stabilizing effect, but too strong a DS term causes phase quenching on the system. We observed that the bias of the dynamical stabilization can, with good accuracy, be removed by extrapolating to zero dynamical stabilization force using a sigmoid fit.

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References (63)

  1. I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo, Nucl. Phys. B, Proc. Suppl. 60, 220 (1998).
  2. Z. Fodor and S. D. Katz, J. High Energy Phys. 03 (2002) 014.
  3. M. Giordano, K. Kapas, S. D. Katz, D. Nogradi, and A. Pasztor, J. High Energy Phys. 05 (2020) 088.
  4. C. R. Allton, S. Ejiri, S. J. Hands, O. Kaczmarek, F. Karsch, E. Laermann, C. Schmidt, and L. Scorzato, Phys. Rev. D 66, 074507 (2002).
  5. R. V. Gavai and S. Gupta, Phys. Rev. D 78, 114503 (2008).
  6. S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, J. High Energy Phys. 01 (2012) 138.
  7. A. Bazavov et al., Phys. Rev. D 95, 054504 (2017).
  8. P. de Forcrand and O. Philipsen, Nucl. Phys. B642, 290 (2002).
  9. M. D’Elia and M.-P. Lombardo, Phys. Rev. D 67, 014505 (2003).
  10. P. Cea, L. Cosmai, and A. Papa, Phys. Rev. D 89, 074512 (2014).
  11. R. Bellwied, S. Borsanyi, Z. Fodor, J. Günther, S. D. Katz, C. Ratti, and K. K. Szabo, Phys. Lett. B 751, 559 (2015).
  12. Z. Fodor, S. D. Katz, and C. Schmidt, J. High Energy Phys. 03 (2007) 121.
  13. G. Endrodi, Z. Fodor, S. D. Katz, D. Sexty, K. K. Szabo, and C. Torok, Phys. Rev. D 98, 074508 (2018).
  14. A. Alexandru, M. Faber, I. Horvath, and K.-F. Liu, Phys. Rev. D 72, 114513 (2005).
  15. S. Kratochvila and P. de Forcrand, Proc. Sci. LAT2005 (2006) 167 [arXiv:hep-lat/0509143].
  16. C. Gattringer, Proc. Sci. LATTICE2013 (2014) 002 [arXiv:1401.7788].
  17. C. Gattringer and K. Langfeld, Int. J. Mod. Phys. A 31, 1643007 (2016).
  18. J. N. Guenther, Eur. Phys. J. A 57, 136 (2021).
  19. J. R. Klauder, Acta Phys. Austriaca Suppl. 25, 251 (1983).
  20. G. Parisi, Phys. Lett. 131B, 393 (1983).
  21. G. Aarts, E. Seiler, and I.-O. Stamatescu, Phys. Rev. D 81, 054508 (2010).
  22. G. Aarts, F. A. James, E. Seiler, and I.-O. Stamatescu, Phys. Lett. B 687, 154 (2010).
  23. G. Aarts, F. A. James, E. Seiler, and I.-O. Stamatescu, Eur. Phys. J. C 71, 1756 (2011).
  24. G. Aarts, F. A. James, J. M. Pawlowski, E. Seiler, D. Sexty, and I.-O. Stamatescu, J. High Energy Phys. 03 (2013) 073.
  25. L. L. Salcedo and E. Seiler, J. Phys. A 52, 035201 (2019).
  26. Z. Cai, X. Dong, and Y. Kuang, SIAM J. Sci. Comput. 43, A685 (2021).
  27. E. Seiler, D. Sexty, and I.-O. Stamatescu, Phys. Rev. D 109, 014509 (2024).
  28. M. Scherzer, E. Seiler, D. Sexty, and I.-O. Stamatescu, Phys. Rev. D 99, 014512 (2019).
  29. M. Scherzer, E. Seiler, D. Sexty, and I. O. Stamatescu, Phys. Rev. D 101, 014501 (2020).
  30. E. Seiler, Phys. Rev. D 102, 094507 (2020).
  31. K. Nagata, J. Nishimura, and S. Shimasaki, Phys. Rev. D 94, 114515 (2016).
  32. K. Nagata, J. Nishimura, and S. Shimasaki, J. High Energy Phys. 05 (2018) 004.
  33. D. Alvestad, R. Larsen, and A. Rothkopf, J. High Energy Phys. 04 (2023) 057.
  34. K. Boguslavski, P. Hotzy, and D. I. Müller, J. High Energy Phys. 06 (2023) 011.
  35. N. M. Lampl and D. Sexty, arXiv:2309.06103.
  36. D. Alvestad, A. Rothkopf, and D. Sexty, Phys. Rev. D 109, L031502 (2024).
  37. E. Seiler, D. Sexty, and I.-O. Stamatescu, Phys. Lett. B 723, 213 (2013).
  38. G. Aarts, L. Bongiovanni, E. Seiler, D. Sexty, and I.-O. Stamatescu, Eur. Phys. J. A 49, 89 (2013).
  39. K. Nagata, J. Nishimura, and S. Shimasaki, Prog. Theor. Exp. Phys. 2016, 013B01 (2016).
  40. Z. Cai, Y. Di, and X. Dong, Commun. Comput. Phys. 27, 1344 (2020).
  41. X. Dong, Z. Cai, and Y. Di, Phys. Rev. D 102, 054518 (2020).
  42. G. Aarts, F. Attanasio, B. Jäger, and D. Sexty, J. High Energy Phys. 09 (2016) 087.
  43. D. Sexty, Phys. Lett. B 729, 108 (2014).
  44. G. Aarts, E. Seiler, D. Sexty, and I.-O. Stamatescu, Phys. Rev. D 90, 114505 (2014).
  45. Z. Fodor, S. D. Katz, D. Sexty, and C. Török, Phys. Rev. D 92, 094516 (2015).
  46. K. Nagata, H. Matsufuru, J. Nishimura, and S. Shimasaki, Proc. Sci. LATTICE2016 (2016) 067 [arXiv:1611.08077].
  47. K. Nagata, J. Nishimura, and S. Shimasaki, Phys. Rev. D 98, 114513 (2018).
  48. J. B. Kogut and D. K. Sinclair, Phys. Rev. D 100, 054512 (2019).
  49. F. Attanasio, B. Jäger, and F. P. G. Ziegler, Eur. Phys. J. A 56, 251 (2020).
  50. T. Yokota, Y. Ito, H. Matsufuru, Y. Namekawa, J. Nishimura, A. Tsuchiya, and S. Tsutsui, J. High Energy Phys. 06 (2023) 061.
  51. D. Sexty, Phys. Rev. D 100, 074503 (2019).
  52. F. Attanasio, B. Jäger, and F. P. G. Ziegler, arXiv:2203.13144.
  53. F. Attanasio and B. Jäger, Eur. Phys. J. C 79, 16 (2019).
  54. Z. Cai, Y. Kuang, and H. K. Tan, Phys. Rev. D 105, 014508 (2022).
  55. P. H. Damgaard and H. Huffel, Phys. Rep. 152, 227 (1987).
  56. M. W. Hansen, M. Mandl, E. Seiler, and D. Sexty, arXiv:2412.17137.
  57. G. Aarts and I.-O. Stamatescu, J. High Energy Phys. 09 (2008) 018.
  58. C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice (Springer, Berlin, 2010), Vol. 788, ISBN [Amazon][WorldCat], [Amazon][WorldCat].
  59. P. de Forcrand, Proc. Sci. LAT2009 (2009) 010 [arXiv:1005.0539].
  60. A. Hasenfratz and D. Toussaint, Nucl. Phys. B371, 539 (1992).
  61. M. Westh Hansen and D. Sexty, Proc. Sci. LATTICE2022 (2023) 163 [arXiv:2212.12029].
  62. M. W. Hansen and D. Sexty (to be published).
  63. T. D. Cohen, Phys. Rev. Lett. 91, 222001 (2003).

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