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Symmetric Mass Generation as a Multicritical Point with Enhanced Symmetry

Sandip Maiti1,2,*, Debasish Banerjee2,3,†, Shailesh Chandrasekharan4,‡, and Marina K. Marinkovic5,§

  • *Contact author: sandipmaiti73@gmail.com
  • †Contact author: D.Banerjee@soton.ac.uk
  • ‡Contact author: sch27@duke.edu
  • §Contact author: marinama@ethz.ch
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Phys. Rev. Lett. 137, 151601 – Published 8 October, 2026

DOI: https://doi.org/10.1103/m3pf-j37b

Abstract

We explore the phase diagram of a lattice fermion model that exhibits three distinct phases: a massless fermion phase, a massive fermion phase with spontaneous symmetry breaking induced by a fermion bilinear condensate, and a massive fermion phase with symmetric mass generation. Using the fermion-bag Monte Carlo method on large cubical lattices, we find evidence for traditional second-order critical points separating the first two and the latter two phases. Remarkably, these critical points appear to merge at a multicritical point with enhanced symmetry when the symmetry breaking parameter is tuned to zero, giving rise to the recently discovered direct second-order transition between the massless and symmetric massive fermion phases.

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Phase diagram of a lattice fermion model with symmetric mass generation

Sandip Maiti, Debasish Banerjee, Shailesh Chandrasekharan, and Marina K. Marinkovic
Phys. Rev. D 114, 074504 (2026)

Article Text

References (38)

  1. D. J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10, 3235 (1974).
  2. A. Hasenfratz, W.-q. Liu, and T. Neuhaus, Phase structure and critical points in a scalar fermion model, Phys. Lett. B 236, 339 (1990).
  3. I.-H. Lee, J. Shigemitsu, and R. E. Shrock, Study of different lattice formulations of a Yukawa model with a real scalar field, Nucl. Phys. B334, 265 (1990).
  4. W. Bock, A. K. De, K. Jansen, J. Jersak, T. Neuhaus, and J. Smit, Phase diagram of a lattice SU(2) X SU(2) scalar fermion model with naive and Wilson fermions, Nucl. Phys. B344, 207 (1990).
  5. K. Slagle, Y.-Z. You, and C. Xu, Exotic quantum phase transitions of strongly interacting topological insulators, Phys. Rev. B 91, 115121 (2015).
  6. V. Ayyar and S. Chandrasekharan, Massive fermions without fermion bilinear condensates, Phys. Rev. D 91, 065035 (2015).
  7. V. Ayyar and S. Chandrasekharan, Origin of fermion masses without spontaneous symmetry breaking, Phys. Rev. D 93, 081701 (2016).
  8. S. Catterall, Fermion mass without symmetry breaking, J. High Energy Phys. 01 (2016) 121.
  9. V. Ayyar and S. Chandrasekharan, Fermion masses through four-fermion condensates, J. High Energy Phys. 10 (2016) 058.
  10. Y.-Y. He, H.-Q. Wu, Y.-Z. You, C. Xu, Z. Y. Meng, and Z.-Y. Lu, Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking, Phys. Rev. B 94, 241111 (2016).
  11. N. Butt, S. Catterall, and G. C. Toga, Symmetric mass generation in lattice gauge theory, Symmetry 13, 2276 (2021).
  12. N. Butt, S. Catterall, and A. Hasenfratz, Symmetric mass generation with four SU(2) doublet fermions, Phys. Rev. Lett. 134, 031602 (2025).
  13. A. Hasenfratz and O. Witzel (Lattice Strong Dynamics Collaboration), Symmetric mass generation, Proc. Sci. EPS-HEP2025 (2026) 467 [arXiv:2511.22678].
  14. S. S. Razamat and D. Tong, Gapped chiral fermions, Phys. Rev. X 11, 011063 (2021).
  15. D. Tong, Comments on symmetric mass generation in 2d and 4d, J. High Energy Phys. 07 (2022) 001.
  16. J. Wang and Y.-Z. You, Symmetric mass generation, Symmetry 14, 1475 (2022).
  17. Y.-Z. You, Y.-C. He, C. Xu, and A. Vishwanath, Symmetric fermion mass generation as deconfined quantum criticality, Phys. Rev. X 8, 011026 (2018).
  18. S. Martin and T. Grover, A perturbative approach to symmetric mass generation, arXiv:2507.23032.
  19. E. Eichten and J. Preskill, Chiral gauge theories on the lattice, Nucl. Phys. B268, 179 (1986).
  20. J. Wang and X.-G. Wen, A solution to the 1+1D gauged chiral fermion problem, Phys. Rev. D 99, 111501 (2018).
  21. Y. Xu and C. Xu, Green’s function zero and symmetric mass generation, arXiv:2103.15865.
  22. M. Zeng, Z. Zhu, J. Wang, and Y.-Z. You, Symmetric mass generation in the 1+1 dimensional chiral fermion 3-4-5-0 model, Phys. Rev. Lett. 128, 185301 (2022).
  23. M. Golterman and Y. Shamir, Propagator zeros and lattice chiral gauge theories, Phys. Rev. Lett. 132, 081903 (2024).
  24. M. Golterman and Y. Shamir, Constraints on the symmetric mass generation paradigm for lattice chiral gauge theories, Phys. Rev. D 113, 014503 (2026).
  25. R. Mouland, D. Tong, and B. Zan, Phases of 2d gauge theories and symmetric mass generation, J. High Energy Phys. 04 (2026) 154.
  26. A. Hasenfratz and T. Neuhaus, Nonperturbative study of the strongly coupled scalar fermion model, Phys. Lett. B 220, 435 (1989).
  27. H. S. Sharatchandra, H. J. Thun, and P. Weisz, Susskind fermions on a Euclidean lattice, Nucl. Phys. B192, 205 (1981).
  28. S. Chandrasekharan, The fermion bag approach to lattice field theories, Phys. Rev. D 82, 025007 (2010).
  29. S. Maiti, D. Banerjee, S. Chandrasekharan, and M. K. Marinkovic, companion paper, Phase diagram of a lattice fermion model with symmetric mass generation, Phys. Rev. D 114, 074504 (2026).
  30. N. Zerf, L. N. Mihaila, P. Marquard, I. F. Herbut, and M. M. Scherer, Four-loop critical exponents for the Gross-Neveu-Yukawa models, Phys. Rev. D 96, 096010 (2017).
  31. F. Gehring, H. Gies, and L. Janssen, Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry, Phys. Rev. D 92, 085046 (2015).
  32. S. Hands, The planar Thirring model with Kähler-Dirac fermions, Symmetry 13, 1523 (2021).
  33. S. Hands, A. Kocic, and J. B. Kogut, Four Fermi theories in fewer than four-dimensions, Ann. Phys. (N.Y.) 224, 29 (1993).
  34. C. Huang, N. Parthenios, M. Ulybyshev, X. Zhang, F. F. Assaad, L. Classen, and Z. Y. Meng, Angle-tuned Gross-Neveu quantum criticality in twisted bilayer graphene, Nat. Commun. 16, 7176 (2025).
  35. B. Hawashin, M. M. Scherer, and L. Janssen, Gross-Neveu-XY quantum criticality in moiré Dirac materials, Phys. Rev. B 111, 205129 (2025).
  36. M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Critical behavior of the three-dimensional XY universality class, Phys. Rev. B 63, 214503 (2001).
  37. N. Butt, S. Catterall, and D. Schaich, SO(4) invariant Higgs-Yukawa model with reduced staggered fermions, Phys. Rev. D 98, 114514 (2018).
  38. , chatgpt 5.2, https://openai.com/chatgpt (2026).

Outline

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Phys. Rev. Lett. 137, 151601– Published 8 October, 2026
  • Received 7 April 2026
  • Revised 6 August 2026
  • Accepted 26 August 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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