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  • Letter
  • Open Access

How quantum fluctuations freeze a classical liquid and then melt it into a topological one

Hao Chen1, Dan Mao1,2, Andrea Kouta Dagnino1, Glenn Wagner1,3, Mark H. Fischer1, Juraj Hasik1, Eun-Ah Kim2,4, and Titus Neupert1,*

  • *Contact author: titus.neupert@physik.uzh.ch
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Phys. Rev. Research 7, L042021 – Published 22 October, 2025

DOI: https://doi.org/10.1103/ydxb-1tfx

Abstract

Topologically ordered quantum liquids are highly sought-after quantum phases of matter, and recently, fractional Chern insulators (FCIs) joined the few experimental realizations of such phases. Here, we ask whether a gapped classical, highly degenerate liquid can be the birthplace of FCIs upon the addition of suitable quantum fluctuations. Two competing tendencies can be anticipated: (1) Following the quantum order-by-disorder paradigm, quantum fluctuations could induce symmetry-breaking (charge) order, or (2) the classical liquid builds up long-range entanglement and turns into a quantum liquid. We study spinless fermions on a honeycomb lattice subject to cluster-charging interactions and introduce quantumness through a Haldane kinetic term, featuring complex second-nearest-neighbor hopping. Based on extensive exact diagonalization calculations and high-order perturbation theory, we find that neither scenario (1) nor (2) prevails, but (1) and (2) manifest sequentially as the kinetic energy is increased. We demonstrate how the gradual lifting of kinematic constraints gives rise to this sequence of phases. Our results relate to the regime of intermediate-scale interactions present in moiré systems, where band projections are not suitable to model FCIs and competing charge-ordered phases have been identified.

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References (44)

  1. E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106, 236802 (2011).
  2. K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011).
  3. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
  4. N. Regnault and B. A. Bernevig, Fractional Chern insulator, Phys. Rev. X 1, 021014 (2011).
  5. Y.-L. Wu, B. A. Bernevig, and N. Regnault, Zoology of fractional Chern insulators, Phys. Rev. B 85, 075116 (2012).
  6. A. M. Läuchli, Z. Liu, E. J. Bergholtz, and R. Moessner, Hierarchy of fractional Chern insulators and competing compressible states, Phys. Rev. Lett. 111, 126802 (2013).
  7. Y.-F. Wang, H. Yao, Z.-C. Gu, C.-D. Gong, and D. N. Sheng, Non-Abelian quantum Hall effect in topological flat bands, Phys. Rev. Lett. 108, 126805 (2012).
  8. S. Kourtis and M. Daghofer, Combined topological and Landau order from strong correlations in Chern bands, Phys. Rev. Lett. 113, 216404 (2014).
  9. S. Kourtis, J. W. F. Venderbos, and M. Daghofer, Fractional Chern insulator on a triangular lattice of strongly correlated t2g electrons, Phys. Rev. B 86, 235118 (2012).
  10. D. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Fractional quantum Hall effect in the absence of Landau levels, Nat. Commun. 2, 389 (2011).
  11. S. Kourtis, T. Neupert, C. Chamon, and C. Mudry, Fractional Chern insulators with strong interactions that far exceed band gaps, Phys. Rev. Lett. 112, 126806 (2014).
  12. A. G. Grushin, J. Motruk, M. P. Zaletel, and F. Pollmann, Characterization and stability of a fermionic ν=1/3 fractional Chern insulator, Phys. Rev. B 91, 035136 (2015).
  13. N. Morales-Durán, N. Wei, J. Shi, and A. H. MacDonald, Magic angles and fractional Chern insulators in twisted homobilayer transition metal dichalcogenides, Phys. Rev. Lett. 132, 096602 (2024).
  14. J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Fractional Chern insulators versus nonmagnetic states in twisted bilayer MoTe2, Phys. Rev. B 109, 045147 (2024).
  15. D. Varjas, A. Abouelkomsan, K. Yang, and E. J. Bergholtz, Topological lattice models with constant Berry curvature, SciPost Phys. 12, 118 (2022).
  16. A. Abouelkomsan, K. Yang, and E. J. Bergholtz, Quantum metric induced phases in moiré materials, Phys. Rev. Res. 5, L012015 (2023).
  17. D. Parker, P. Ledwith, E. Khalaf, T. Soejima, J. Hauschild, Y. Xie, A. Pierce, M. P. Zaletel, A. Yacoby, and A. Vishwanath, Field-tuned and zero-field fractional Chern insulators in magic angle graphene, arXiv:2112.13837 [cond-mat].
  18. P. Wilhelm, T. C. Lang, and A. M. Läuchli, Interplay of fractional Chern insulator and charge density wave phases in twisted bilayer graphene, Phys. Rev. B 103, 125406 (2021).
  19. V. Crépel and L. Fu, Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides, Phys. Rev. B 107, L201109 (2023).
  20. T. Lu and L. H. Santos, Fractional Chern insulators in twisted bilayer MoTe2: A composite fermion perspective, Phys. Rev. Lett. 133, 186602 (2024).
  21. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional Chern insulators and the W∞ algebra, Phys. Rev. B 85, 241308 (2012).
  22. Z. Liu and E. J. Bergholtz, From fractional Chern insulators to abelian and non-abelian fractional quantum Hall states: Adiabatic continuity and orbital entanglement spectrum, Phys. Rev. B 87, 035306 (2013).
  23. M. Claassen, C. H. Lee, R. Thomale, X.-L. Qi, and T. P. Devereaux, Position-momentum duality and fractional quantum Hall effect in Chern insulators, Phys. Rev. Lett. 114, 236802 (2015).
  24. J. Wang, J. Cano, A. J. Millis, Z. Liu, and B. Yang, Exact Landau level description of geometry and interaction in a flatband, Phys. Rev. Lett. 127, 246403 (2021).
  25. Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional Chern insulator in moiré MoTe2, Nature (London) 622, 69 (2023).
  26. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe et al., Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  27. Z. Ji, H. Park, M. E. Barber, C. Hu, K. Watanabe, T. Taniguchi, J.-H. Chu, X. Xu, and Z.-X. Shen, Local probe of bulk and edge states in a fractional Chern insulator, Nature (London) 635, 578 (2024).
  28. Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo-Herrero, and A. Yacoby, Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 600, 439 (2021).
  29. S. H. Aronson, T. Han, Z. Lu, Y. Yao, J. P. Butler, K. Watanabe, T. Taniguchi, L. Ju, and R. C. Ashoori, Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice, Phys. Rev. X 15, 031026 (2025).
  30. K. Zhang, D. Mao, E.-A. Kim, and R. Moessner, Bionic fractionalization in the trimer model of twisted bilayer graphene, Commun. Mater. 6, 124 (2025).
  31. H. C. Po, L. Zou, A. Vishwanath, and T. Senthil, Origin of mott insulating behavior and superconductivity in twisted bilayer graphene, Phys. Rev. X 8, 031089 (2018).
  32. J. Kang and O. Vafek, Strong coupling phases of partially filled twisted bilayer graphene narrow bands, Phys. Rev. Lett. 122, 246401 (2019).
  33. Y.-H. Zhang, D. Mao, and T. Senthil, Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model, Phys. Rev. Res. 1, 033126 (2019).
  34. N. Astrakhantsev, G. Wagner, T. Westerhout, T. Neupert, and M. H. Fischer, Understanding symmetry breaking in twisted bilayer graphene from cluster constraints, Phys. Rev. Res. 5, 043214 (2023).
  35. A. Verberkmoes and B. Nienhuis, Triangular trimers on the triangular lattice: An exact solution, Phys. Rev. Lett. 83, 3986 (1999).
  36. K. Zhang, Y. Zhang, L. Fu, and E.-A. Kim, Fractional correlated insulating states at one-third filled magic angle twisted bilayer graphene, Commun. Phys. 5, 250 (2022).
  37. D. S. Rokhsar and S. A. Kivelson, Superconductivity and the quantum hard-core dimer gas, Phys. Rev. Lett. 61, 2376 (1988).
  38. R. Moessner, S. L. Sondhi, and E. Fradkin, Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories, Phys. Rev. B 65, 024504 (2001).
  39. C. Repellin, B. A. Bernevig, and N. Regnault, Z2 fractional topological insulators in two dimensions, Phys. Rev. B 90, 245401 (2014).
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ydxb-1tfx for additional details.
  41. D. Mao, K. Zhang, and E.-A. Kim, Fractionalization in fractional correlated insulating states at n±1/3 filled twisted bilayer graphene, Phys. Rev. Lett. 131, 106801 (2023).
  42. S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Ann. Phys. 326, 2793 (2011).
  43. K. Slagle and Y. B. Kim, Fracton topological order from nearest-neighbor two-spin interactions and dualities, Phys. Rev. B 96, 165106 (2017).
  44. S. Musser, M. Cheng, and T. Senthil, Fractionalization as an alternate to charge ordering in electronic insulators, Phys. Rev. B 111, 235108 (2025).

Outline

Information

Phys. Rev. Research 7, L042021– Published 22 October, 2025
  • Received 2 May 2025
  • Accepted 25 September 2025
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