- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Instability of Nagaoka state and quantum phase transition via kinetic frustration control

Prakash Sharma1,2,*, Yang Peng2,3, Donna N. Sheng2, Hitesh J. Changlani4,5, and Yao Wang1

  • *Contact author: sharmaprakash078@gmail.com
PDF

Phys. Rev. Research 8, 023070 – Published 23 April, 2026

DOI: https://doi.org/10.1103/z4gs-c6h6

Abstract

We investigate the Nagaoka-Thouless ferromagnetic instability in the strongly interacting t−t′ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin polaron when the kinetic frustration t′/t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the Nagaoka ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite hole density via frustration-induced magnon band deformation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

  1. Y. Nagaoka, Ferromagnetism in a narrow, almost half-filled s band, Phys. Rev. 147, 392 (1966).
  2. D. Thouless, Exchange in solid He3 and the Heisenberg Hamiltonian, Proc. Phys. Soc. 86, 893 (1965).
  3. E. C. Stoner, Collective electron ferromagnetism, Proc. R. Soc. London A 165, 372 (1938).
  4. A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science 365, 605 (2019).
  5. K. R. Kittilstved, D. A. Schwartz, A. C. Tuan, S. M. Heald, S. A. Chambers, and D. R. Gamelin, Direct kinetic correlation of carriers and ferromagnetism in Co2+:ZnO, Phys. Rev. Lett. 97, 037203 (2006).
  6. K. F. Mak and J. Shan, Semiconductor moiré materials, Nat. Nanotechnol. 17, 686 (2022).
  7. F. Wu, T. Lovorn, E. Tutuc, and A. H. MacDonald, Hubbard model physics in transition metal dichalcogenide moiré bands, Phys. Rev. Lett. 121, 026402 (2018).
  8. K. P. Nuckolls and A. Yazdani, A microscopic perspective on moiré materials, Nat. Rev. Mater. 9, 460 (2024).
  9. S. Xie et al., Strong interlayer interactions in bilayer and trilayer moiré superlattices, Sci. Adv. 8, eabk1911 (2022).
  10. C. Zener, Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure, Phys. Rev. 82, 403 (1951).
  11. Y. Tokura and N. Nagaosa, Orbital physics in transition-metal oxides, Science 288, 462 (2000).
  12. E. Dagotto, T. Hotta, and A. Moreo, Colossal magnetoresistant materials: The key role of phase separation, Phys. Rep. 344, 1 (2001).
  13. Y. Tang et al., Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices, Nature (London) 579, 353 (2020).
  14. L. Ciorciaro et al., Kinetic magnetism in triangular moiré materials, Nature (London) 623, 509 (2023).
  15. M. L. Prichard, B. M. Spar, I. Morera, E. Demler, Z. Z. Yan, and W. S. Bakr, Directly imaging spin polarons in a kinetically frustrated Hubbard system, Nature (London) 629, 323 (2024).
  16. M. Lebrat, M. Xu, L. H. Kendrick, A. Kale, Y. Gang, P. Seetharaman, I. Morera, E. Khatami, E. Demler, and M. Greiner, Observation of Nagaoka polarons in a Fermi–Hubbard quantum simulator, Nature (London) 629, 317 (2024).
  17. J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Imaging magnetic polarons in the doped Fermi–Hubbard model, Nature (London) 572, 358 (2019).
  18. K. Lee, P. Sharma, O. Vafek, and H. J. Changlani, Triangular lattice Hubbard model physics at intermediate temperatures, Phys. Rev. B 107, 235105 (2023).
  19. I. Morera, M. Kanász-Nagy, T. Smolenski, L. Ciorciaro, A. Imamoğlu, and E. Demler, High-temperature kinetic magnetism in triangular lattices, Phys. Rev. Res. 5, L022048 (2023).
  20. R. Samajdar and R. N. Bhatt, Nagaoka ferromagnetism in doped Hubbard models in optical lattices, Phys. Rev. A 110, L021303 (2024).
  21. M. Xu, L. H. Kendrick, A. Kale, Y. Gang, G. Ji, R. T. Scalettar, M. Lebrat, and M. Greiner, Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator, Nature (London) 620, 971 (2023).
  22. G. Li, A. E. Antipov, A. N. Rubtsov, S. Kirchner, and W. Hanke, Competing phases of the Hubbard model on a triangular lattice: Insights from the entropy, Phys. Rev. B 89, 161118(R) (2014).
  23. D. Pereira and E. J. Mueller, Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models, Phys. Rev. B 112, 245120 (2025).
  24. Y. Zhang and L. Fu, Pseudogap metal and magnetization plateau from doping moiré Mott insulator, SciPost Phys. Core 6, 038 (2023).
  25. J. O. Haerter and B. S. Shastry, Kinetic antiferromagnetism in the triangular lattice, Phys. Rev. Lett. 95, 087202 (2005).
  26. C. N. Sposetti, B. Bravo, A. E. Trumper, C. J. Gazza, and L. O. Manuel, Classical antiferromagnetism in kinetically frustrated electronic models, Phys. Rev. Lett. 112, 187204 (2014).
  27. G. Martinez and P. Horsch, Spin polarons in the t-J model, Phys. Rev. B 44, 317 (1991).
  28. M. Davydova, Y. Zhang, and L. Fu, Itinerant spin polaron and metallic ferromagnetism in semiconductor moiré superlattices, Phys. Rev. B 107, 224420 (2023).
  29. S.-S. Zhang, W. Zhu, and C. D. Batista, Pairing from strong repulsion in triangular lattice Hubbard model, Phys. Rev. B 97, 140507(R) (2018).
  30. R. C. Newby and E. Khatami, Finite-temperature kinetic ferromagnetism in the square-lattice Hubbard model, Phys. Rev. B 111, 245120 (2025).
  31. Z. Tao, W. Zhao, B. Shen, T. Li, P. Knüppel, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Observation of spin polarons in a frustrated moiré Hubbard system, Nat. Phys. 20, 783 (2024).
  32. W. Barford and J. H. Kim, Spinless fermions on frustrated lattices in a magnetic field, Phys. Rev. B 43, 559 (1991).
  33. J. Merino, B. J. Powell, and R. H. McKenzie, Ferromagnetism, paramagnetism, and a Curie-Weiss metal in an electron-doped Hubbard model on a triangular lattice, Phys. Rev. B 73, 235107 (2006).
  34. F. T. Lisandrini, B. Bravo, A. E. Trumper, L. O. Manuel, and C. J. Gazza, Evolution of Nagaoka phase with kinetic energy frustrating hopping, Phys. Rev. B 95, 195103 (2017).
  35. H. Tasaki, Extension of Nagaoka's theorem on the large-U Hubbard model, Phys. Rev. B 40, 9192 (1989).
  36. See Supplemental Material at https://link.aps.org/supplemental/10.1103/z4gs-c6h6 for detailed derivation of kinetic magnetism in triangular geometry, analytic solution for one-hole-one-magnon states in 1D and 2D limits, and the probability distribution of the one-hole-one-magnon states.
  37. S. U. Pillai, T. Suel, and S. Cha, The Perron-Frobenius theorem: Some of its applications, IEEE Signal Process. Mag. 22, 62 (2005).
  38. M. Fishman, S. R. White, and E. M. Stoudenmire, The itensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  39. I. Ivantsov, H. B. Xavier, A. Ferraz, and E. Kochetov, Stable and metastable kinetic ferromagnetism on a ring, Phys. Rev. B 101, 195107 (2020).
  40. G.-S. Tian, The Nagaoka state in the one-hand Hubbard model with two and more holes, J. Phys. A: Math. Gen. 24, 513 (1991).
  41. G. Carleo, S. Moroni, F. Becca, and S. Baroni, Itinerant ferromagnetic phase of the Hubbard model, Phys. Rev. B 83, 060411(R) (2011).
  42. L. Liu, H. Yao, E. Berg, S. R. White, and S. A. Kivelson, Phases of the infinite U Hubbard model on square lattices, Phys. Rev. Lett. 108, 126406 (2012).
  43. X. Y. Zhang, E. Abrahams, and G. Kotliar, Quantum Monte Carlo algorithm for constrained fermions: Application to the infinite-U Hubbard model, Phys. Rev. Lett. 66, 1236 (1991).
  44. B. S. Shastry, H. R. Krishnamurthy, and P. W. Anderson, Instability of the Nagaoka ferromagnetic state of the U = ∞ Hubbard model, Phys. Rev. B 41, 2375 (1990).
  45. F. Becca and S. Sorella, Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model, Phys. Rev. Lett. 86, 3396 (2001).
  46. P. Sharma, Y. Peng, D. Sheng, H. Changlani, and Y. Wang, Instability of nagaoka state and quantum phase transition via kinetic frustration control [Data set], Zenodo (2026), doi: 10.5281/zenodo.19297472.

Outline

Information

Phys. Rev. Research 8, 023070– Published 23 April, 2026
  • Received 25 August 2025
  • Accepted 24 March 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation