- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition

Tevž Lotrič and Steven H. Simon

PDF

Phys. Rev. Lett. 136, 096601 – Published 3 March, 2026

DOI: https://doi.org/10.1103/l9rp-y68y

Abstract

We consider a model of hard-core bosons on a lattice half-filling a Chern band such that the system has a continuous transition between a fractional Chern insulator (FCI) and a superfluid state (SF) depending on the bandwidth to bandspacing ratio. We construct a parton-inspired trial wave function Ansatz for the ground states that has remarkably high overlap with exact diagonalization in both phases and throughout the phase transition. Our Ansatz is stable to adding some bosonic interactions beyond the on-site hard-core constraint. We confirm that the transition is well described by a projective translation symmetry-protected multiple parton bandgap closure, as has been previously predicted. However, unlike prior work, we find that our wave functions require anomalous (BCS-like) parton correlations to describe the phase transition and SF phase accurately.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional quantum Hall physics in topological flat bands, C.R. Phys. 14, 816 (2013).
  2. E. J. Bergholtz and Z. Liu, Topological flat band models and fractional Chern insulators, Int. J. Mod. Phys. B 27, 1330017 (2013).
  3. Z. Liu and E. J. Bergholtz, Recent developments in fractional Chern insulators, in Encyclopedia of Condensed Matter Physics (2nd ed.), edited by T. Chakraborty (Academic Press, Oxford, 2024), pp. 515–538.
  4. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
  5. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2, Phys. Rev. X 13, 031037 (2023).
  6. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  7. R. Roy, Band geometry of fractional topological insulators, Phys. Rev. B 90, 165139 (2014).
  8. P. J. Ledwith, A. Vishwanath, and D. E. Parker, Vortexability: A unifying criterion for ideal fractional Chern insulators, Phys. Rev. B 108, 205144 (2023).
  9. M. Fujimoto, D. E. Parker, J. Dong, E. Khalaf, A. Vishwanath, and P. Ledwith, Higher vortexability: Zero-field realization of higher Landau levels, Phys. Rev. Lett. 134, 106502 (2025).
  10. E. Kapit and E. Mueller, Exact parent hamiltonian for the quantum Hall states in a lattice, Phys. Rev. Lett. 105, 215303 (2010).
  11. J. Motruk and F. Pollmann, Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold-atom model, Phys. Rev. B 96, 165107 (2017).
  12. T.-S. Zeng, Phase transitions of bosonic fractional quantum Hall effect in topological flat bands, Phys. Rev. B 103, 085122 (2021).
  13. H. Lu, H.-Q. Wu, B.-B. Chen, and Z. Y. Meng, Continuous transition between bosonic fractional Chern insulator and superfluid, Phys. Rev. Lett. 134, 076601 (2025).
  14. M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum Hall and superfluid states, Phys. Rev. B 89, 235116 (2014).
  15. A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall states of atoms in optical lattices, Phys. Rev. Lett. 94, 086803 (2005).
  16. M. Barkeshli, N. Y. Yao, and C. R. Laumann, Continuous preparation of a fractional Chern insulator, Phys. Rev. Lett. 115, 026802 (2015).
  17. X.-Y. Song, Y.-H. Zhang, and T. Senthil, Phase transitions out of quantum Hall states in moiré materials, Phys. Rev. B 109, 085143 (2024).
  18. J. Y. Lee, C. Wang, M. P. Zaletel, A. Vishwanath, and Y.-C. He, Emergent multi-flavor QED3 at the plateau transition between fractional Chern insulators: Applications to graphene heterostructures, Phys. Rev. X 8, 031015 (2018).
  19. X.-Y. Song and Y.-H. Zhang, Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator, SciPost Phys. 15, 215 (2023).
  20. Y.-F. Wang, Z.-C. Gu, C.-D. Gong, and D. N. Sheng, Fractional quantum Hall effect of hard-core bosons in topological flat bands, Phys. Rev. Lett. 107, 146803 (2011).
  21. T. Neupert, L. Santos, C. Chamon, and C. Mudry, Fractional quantum Hall states at zero magnetic field, Phys. Rev. Lett. 106, 236804 (2011).
  22. K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/l9rp-y68y for additional calculation details, which include Refs. [24–31].
  24. M. E. Peskin, Mandelstam-’t Hooft duality in Abelian lattice models, Ann. Phys. (N.Y.) 113, 122 (1978).
  25. C. Dasgupta and B. I. Halperin, Phase transition in a lattice model of superconductivity, Phys. Rev. Lett. 47, 1556 (1981).
  26. N. Seiberg, T. Senthil, C. Wang, and E. Witten, A duality web in 2+1 dimensions and condensed matter physics, Ann. Phys. (Amsterdam) 374, 395 (2016).
  27. G. J. Henderson, G. Möller, and S. H. Simon, Energy minimization of paired composite fermion wave functions in the spherical geometry, Phys. Rev. B 108, 245128 (2023).
  28. G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science 355, 602 (2017).
  29. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  30. R. G. Xu, T. Okubo, S. Todo, and M. Imada, Optimized implementation for calculation and fast-update of Pfaffians installed to the open-source fermionic variational solver mVMC, Comput. Phys. Commun. 277, 108375 (2022).
  31. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  32. X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, New York, 2007).
  33. X.-G. Wen, Projective construction of non-Abelian quantum Hall liquids, Phys. Rev. B 60, 8827 (1999).
  34. J. McGreevy, B. Swingle, and K.-A. Tran, Wave functions for fractional Chern insulators, Phys. Rev. B 85, 125105 (2012).
  35. T. Wang, X.-Y. Song, M. P. Zaletel, and T. Senthil, Emergent QED3 at the bosonic laughlin state to superfluid transition, arXiv:2507.07611.

  36. This translates to requiring O to be a singlet with respect to the SU(2) gauge field in the field-theoretical approach.

  37. N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
  38. A julia implementation of the VMC code is publicly available online, https://github.com/tevz-lotric/VMCpartonTrialWF.
  39. W.-W. Luo, A.-L. He, Y. Zhou, Y.-F. Wang, and C.-D. Gong, Quantum phase transitions in a ν=12 bosonic fractional Chern insulator, Phys. Rev. B 102, 155120 (2020).
  40. H. Lu, H.-Q. Wu, B.-B. Chen, and Z. Y. Meng, Vestigial gapless boson density wave emerging between ν=1/2 fractional Chern insulator and finite-momentum supersolid, Phys. Rev. B 113, 035141 (2026).

Outline

Information

Phys. Rev. Lett. 136, 096601– Published 3 March, 2026
  • Received 9 May 2025
  • Revised 17 August 2025
  • Accepted 12 February 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