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Bulletin of the American Physical Society

Variational study of bosonic phases in two dimensions: fractional Chern insulator, Mott insulator and superfluid

Bryan K. Clark, Hassan Shapourian

Published Mar 2, 2015• 0 citations
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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.

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We numerically study the model wave-functions for a system of hard core bosons at half filling on a square lattice. The candidate wave-functions are based on the projective construction approach [1] where a boson is decomposed into two (slave) fermions, each described by a Chern insulator model. Our results confirm that the wave-functions demonstrate the following phases: the superfluid, the Mott insulator and the fractional Chern insulator. In addition, we find that the wave-functions can be continuously tuned from one phase to another by varying the parameters of slave particles. We further propose a microscopic Hamiltonian with a rich phase diagram which variationally supports all the aforementioned phases in different regimes of parameters. The critical behavior across the phase boundaries is investigated and the critical exponents are computed.
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.
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.