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  • Open Access

Boundary critical behavior of the Gross-Neveu-Yukawa model

Andrei A. Fedorenko1,* and Ilya A. Gruzberg2,†

  • *Contact author: andrey.fedorenko@ens-lyon.fr
  • †Contact author: gruzberg.1@osu.edu
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Phys. Rev. D 114, 025017 – Published 22 July, 2026

DOI: https://doi.org/10.1103/2rm3-ggl3

Abstract

We study the critical behavior of the semi-infinite Gross-Neveu-Yukawa model, a quantum field theory describing Dirac fermions interacting with bosonic fields via a Yukawa coupling. We consider Neumann and Dirichlet boundary conditions for the bosonic fields, and the most general boundary conditions for the fermions that preserve unitarity, conformal invariance, and charge conjugation symmetry. We analyze the phase diagram and identify distinct fixed points corresponding to different universality classes of boundary critical behavior. The associated boundary critical exponents, which govern the scaling behavior and crossover phenomena, are computed to one-loop order. We also discuss the relevance of our results to the semi-infinite pseudoscalar Yukawa model.

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References (78)

  1. D. Poland, S. Rychkov, and A. Vichi, Rev. Mod. Phys. 91, 015002 (2019).
  2. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).
  3. J. Cayssol, C. R. Phys. 14, 760 (2013).
  4. N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
  5. H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1986), Vol. 10.
  6. M. A. Metlitski, SciPost Phys. 12, 131 (2022).
  7. J. Padayasi, A. Krishnan, M. A. Metlitski, I. A. Gruzberg, and M. Meineri, SciPost Phys. 12, 190 (2022).
  8. F. Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021).
  9. F. Parisen Toldin and M. A. Metlitski, Phys. Rev. Lett. 128, 215701 (2022).
  10. Y. Sun and J.-P. Lv, Phys. Rev. B 106, 224502 (2022).
  11. Y.-H. Zhang, Z. Zhu, and A. Vishwanath, Phys. Rev. X 13, 031023 (2023).
  12. 50 Years of Anderson Localization, edited by E. Abrahams (World Scientific, Singapore, 2010).
  13. F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008).
  14. A. R. Subramaniam, I. A. Gruzberg, A. W. W. Ludwig, F. Evers, A. Mildenberger, and A. D. Mirlin, Phys. Rev. Lett. 96, 126802 (2006).
  15. A. Mildenberger, A. R. Subramaniam, R. Narayanan, F. Evers, I. A. Gruzberg, and A. D. Mirlin, Phys. Rev. B 75, 094204 (2007).
  16. H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. Lett. 98, 156802 (2007).
  17. H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Physica (Amsterdam) 40E, 1404 (2008).
  18. H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. Lett. 101, 116802 (2008).
  19. A. R. Subramaniam, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. B 78, 245105 (2008).
  20. S. S. Babkin, J. F. Karcher, I. S. Burmistrov, and A. D. Mirlin, Phys. Rev. B 108, 104205 (2023).
  21. S. S. Babkin and I. S. Burmistrov, Phys. Rev. B 108, 205429 (2023).
  22. S. V. Syzranov and L. Radzihovsky, Annu. Rev. Condens. Matter Phys. 9, 35 (2018).
  23. B. Roy and S. Das Sarma, Phys. Rev. B 90, 241112(R) (2014); 93, 119911(E) (2016).
  24. T. Louvet, D. Carpentier, and A. A. Fedorenko, Phys. Rev. B 94, 220201(R) (2016).
  25. S. V. Syzranov, P. M. Ostrovsky, V. Gurarie, and L. Radzihovsky, Phys. Rev. B 93, 155113 (2016).
  26. B. Sbierski, G. Pohl, E. J. Bergholtz, and P. W. Brouwer, Phys. Rev. Lett. 113, 026602 (2014).
  27. B. Sbierski, K. S. C. Decker, and P. W. Brouwer, Phys. Rev. B 94, 220202(R) (2016).
  28. E. Fradkin, Phys. Rev. B 33, 3263 (1986).
  29. B. Roy, V. Juričić, and S. Das Sarma, Sci. Rep. 6, 32446 (2016).
  30. P. Goswami and S. Chakravarty, Phys. Rev. Lett. 107, 196803 (2011).
  31. P. Hosur, S. A. Parameswaran, and A. Vishwanath, Phys. Rev. Lett. 108, 046602 (2012).
  32. Y. Ominato and M. Koshino, Phys. Rev. B 89, 054202 (2014).
  33. C.-Z. Chen, J. Song, H. Jiang, Q.-F. Sun, Z. Wang, and X. C. Xie, Phys. Rev. Lett. 115, 246603 (2015).
  34. A. Altland and D. Bagrets, Phys. Rev. Lett. 114, 257201 (2015), Phys. Rev. B 93, 075113 (2016).
  35. A. L. Szabó and B. Roy, Phys. Rev. Res. 2, 043197 (2020).
  36. K. Kobayashi, T. Ohtsuki, K.-I. Imura, and I. F. Herbut, Phys. Rev. Lett. 112, 016402 (2014).
  37. B. Sbierski, E. J. Bergholtz, and P. W. Brouwer, Phys. Rev. B 92, 115145 (2015).
  38. S. Liu, T. Ohtsuki, and R. Shindou, Phys. Rev. Lett. 116, 066401 (2016).
  39. S. Bera, J. D. Sau, and B. Roy, Phys. Rev. B 93, 201302(R) (2016).
  40. B. Fu, W. Zhu, Q. Shi, Q. Li, J. Yang, and Z. Zhang, Phys. Rev. Lett. 118, 146401 (2017).
  41. B. Sbierski, K. A. Madsen, P. W. Brouwer, and C. Karrasch, Phys. Rev. B 96, 064203 (2017).
  42. B. Roy, R.-J. Slager, and V. Juričić, Phys. Rev. X 8, 031076 (2018).
  43. I. Balog, D. Carpentier, and A. A. Fedorenko, Phys. Rev. Lett. 121, 166402 (2018).
  44. T. Louvet, D. Carpentier, and A. A. Fedorenko, Phys. Rev. B 95, 014204 (2017).
  45. B. Sbierski and C. Fräßdorf, Phys. Rev. B 99, 020201(R) (2019).
  46. J. Klier, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B 100, 125160 (2019).
  47. E. Brillaux, D. Carpentier, and A. A. Fedorenko, Phys. Rev. B 100, 134204 (2019).
  48. E. Brillaux and A. A. Fedorenko, Phys. Rev. B 103, L081405 (2021).
  49. E. Brillaux, A. A. Fedorenko, and I. A. Gruzberg, Phys. Rev. B 109, 174204 (2024).
  50. R.-X. Miao, C.-S. Chu, and W.-Z. Guo, Phys. Rev. D 96, 046005 (2017).
  51. C. P. Herzog and K.-W. Huang, J. High Energy Phys. 10 (2017) 189.
  52. M. A. Shpot, J. High Energy Phys. 01 (2021) 055.
  53. C. P. Herzog and V. Schaub, Phys. Rev. D 109, L061701 (2024).
  54. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 5th ed. (Oxford University Press, Oxford, 2021).
  55. B. Rosenstein, H.-L. Yu, and A. Kovner, Phys. Lett. B 314, 381 (1993).
  56. L. Fei, S. Giombi, I. R. Klebanov, and G. Tarnopolsky, Prog. Theor. Exp. Phys. 2016, 12C105 (2016).
  57. L. N. Mihaila, N. Zerf, B. Ihrig, I. F. Herbut, and M. M. Scherer, Phys. Rev. B 96, 165133 (2017).
  58. N. Zerf, L. N. Mihaila, P. Marquard, I. F. Herbut, and M. M. Scherer, Phys. Rev. D 96, 096010 (2017).
  59. B. Ihrig, L. N. Mihaila, and M. M. Scherer, Phys. Rev. B 98, 125109 (2018).
  60. R. S. Erramilli, L. V. Iliesiu, P. Kravchuk, A. Liu, D. Poland, and D. Simmons-Duffin, J. High Energy Phys. 02 (2023) 036.
  61. L. Rosa, P. Vitale, and C. Wetterich, Phys. Rev. Lett. 86, 958 (2001).
  62. B. Knorr, Phys. Rev. B 94, 245102 (2016).
  63. S. Chandrasekharan and A. Li, Phys. Rev. D 88, 021701 (2013).
  64. S. Giombi, E. Helfenberger, and H. Khanchandani, J. High Energy Phys. 07 (2022) 018.
  65. C. P. Herzog and V. Schaub, J. High Energy Phys. 02 (2023) 129.
  66. H. Jiang, Y. Ge, and S.-K. Jian, Phys. Rev. Lett. 135, 141602 (2025).
  67. X. Shen, Z. Wu, and S.-K. Jian, Phys. Rev. B 112, L041118 (2025).
  68. Y. Ge, H. Jiang, H. Yao, and S.-K. Jian, arXiv:2510.05230.
  69. A. N. Redlich, Phys. Rev. D 29, 2366 (1984).
  70. S. Biswas and G. W. Semenoff, J. High Energy Phys. 10 (2022) 045.
  71. E. McCann and V. I. Fal’ko, J. Phys. Condens. Matter 16, 2371 (2004).
  72. A. R. Akhmerov and C. W. J. Beenakker, Phys. Rev. B 77, 085423 (2008).
  73. O. Shtanko and L. Levitov, Proc. Natl. Acad. Sci. U.S.A. 115, 5908 (2018).
  74. K. Hashimoto, T. Kimura, and X. Wu, Prog. Theor. Exp. Phys. 2017, 053I01 (2017).
  75. Z. Faraei, T. Farajollahpour, and S. A. Jafari, Phys. Rev. B 98, 195402 (2018).
  76. A. Rohim and K. Yamamoto, Prog. Theor. Exp. Phys. 2021, 113B01 (2021).
  77. O. Diatlyk, S. Giombi, and Z. Sun, arXiv:2606.07510.
  78. L. Brey and H. A. Fertig, Phys. Rev. B 73, 235411 (2006).

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Phys. Rev. D 114, 025017– Published 22 July, 2026
  • Received 22 March 2026
  • Accepted 26 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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