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.
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.
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.
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.
The roton-triggered charge-density-wave (CDW)is widely studied in fractional quantum Hall (FQH) and fractional Chern insulator (FCI) systems, and there also exist field theoretical and numerical realizations of continuous transition from FCI to superfluid (SF). However, the theory and numerical explorations of the transition between FCI and supersolid (SS) are still lacking. In this work, we study the topological flat-band lattice models with ν = 1/2 hard-core bosons, where the previous studies have discovered the existence of FCI states and possible direct FCI-SS transitions. While the FCI is robust, we find the direct FCI-SS transition is absent, and there exist more intriguing scenarios. In the case of checkerboard lattice, we find an intermediate gapless CDW state without SF, sandwiched between FCI and SS. This novel state is triggered by the roton instability in FCI and it further continuously brings about the intertwined finite-momentum SF fluctuation when the CDW order is strong enough, eventually transiting into an unconventional finite-momentum SS state. The intermediate gapless CDW state is a vestige from the SS state, since the increasing quantum fluctuation melts only the Larkin-Ovchinnikov-type SF order in SS but its (secondary) product -- the CDW order -- survives. On honeycomb lattice, we find no evidence of SS, but discover an interesting sequence of FCI-Solid I-Solid II transitions, with both solids incompressible. Moreover, in contrast to previous single-roton condensation, this sequence of FCI-Solid I-Solid II transitions is triggered by the softening of multi-roton modes in FCI. Considering the intertwined wave vectors of the CDW orders, Solid I is a vestige of Solid II. Our work provides new horizon not only for the quantum phase transitions in FCI but also for the intertwined orders and gapless states in bosonic systems, which will inspire future studies.
Non-Abelian (NA) fractional topological states with quasiparticles obeying NA braiding statistics have attracted intensive attention for both their fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable $\ensuremath{\nu}=1$ bosonic NA-FCI is characterized by edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a $\ensuremath{\nu}=1/2$ Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.
Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena to the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states in disk geometry with the aid of the generalized Pauli principle (GPP) and Jack polynomials. Compared with the ground state by the exact diagonalization method, the wave-function overlap is higher than 0.97, even when the Hilbert space dimension is as large as 3 × 10 6 . We also use the GPP and the Jack polynomials to construct edge excitations for the fermionic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.
We study the extended Bose-Hubbard model on the square lattice at half-filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a two-parameter family of wave functions based on the parton construction which can describe both topological and broken symmetry phases on equal footing. In addition, our wave functions resolve long standing issues with more conventional short-range Jastrow wave functions. Using this variational ansatz, we show that a spontaneous time-reversal symmetry-breaking fractional Chern insulator is energetically favored over a critical region between two superfluid phases. In verifying the properties of these parton wave functions we exemplify a more robust way to identify topology through the Hall conductance.