Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid.

The properties of fractional Chern insulator (FCI) phases and the phase transitions between FCIs and Mott insulators in bosonic systems are well studied. The continuous transitions between FCI and superfluids (SFs), however, despite the inspiring field theoretical predictions [M. Barkeshli and J. McGreevy, Phys. Rev. B 89, 235116 (2014)PRBMDO1098-012110.1103/PhysRevB.89.235116; M. Barkeshli and J. McGreevy, Phys. Rev. B 86, 075136 (2012)PRBMDO1098-012110.1103/PhysRevB.86.075136; M. Barkeshli et al., Phys. Rev. Lett. 115, 026802 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.026802; X.-Y. Song et al., Phys. Rev. B 109, 085143 (2024)PRBMDO2469-995010.1103/PhysRevB.109.085143; and X.-Y. Song and Y.-H. Zhang, SciPost Phys. 15, 215 (2023)2542-465310.21468/SciPostPhys.15.5.215], have not been directly verified. The existing numerical results of the FCI-SF transition are either indirect or clearly first order. Here, by simply tuning the bandwidth of the Haldane honeycomb lattice model, we find direct transitions from a bosonic FCI at ν=1/2 filling of a flat Chern band to two SF states with bosons condensed at momenta M or Γ, respectively. While the FCI-SF(M) transition is first order, the FCI-SF(Γ) transition is found to be continuous, and the bipartite entanglement entropy at the critical point with the area-law scaling is consistent with the critical theories. Through finite-size criticality analysis, the obtained critical exponents β≈0.35(5) and ν≈0.62(12) are both compatible with those of the 3D XY universality class within numerical uncertainty and possibly more exotic beyond-Landau ones. This Letter thence presents a direct numerical demonstration of a continuous FCI-SF transition between a topologically ordered phase and a spontaneous continuous symmetry-breaking phase, and further indicates the zero-field bosonic FCI might be realized from a SF state by gradually flattening the dispersion of the Chern band, through the (quasi)adiabatic preparation in ultracold atom systems.