We show that the optimal trial wave function of a fractional Chern insulator depends on the form of its interaction. The gauge of single particle Bloch bases for constructing the optimal wave trail function is obtained by applying the variational principle proposed by Zhang et al.. We consider a short-range interaction, the Coulomb interaction, and an interpolation between them, and determine the evolution of the optimal gauge with the different interactions. We compare the optimal gauge with those proposed by Qi and Wu et al., and find that Wu et al.'s gauge is close to the optimal gauge when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases. Both the gauges deviate significantly from the optimal gauge when the short range component of the interaction becomes more prominent.
The many-body ground state wave function of a fractional Chern insulator (FCI) can be constructed by mapping a fractional quantum Hall state to a FCI state through a substitution of the Bloch state of the flat Chern band for the magnetic Bloch state of the Landau level. There is a gauge freedom in choosing the single particle Bloch basis of the flat Chern band. Instead of considering only one form of interaction in FCI when choosing the gauge as done in previous works, we determine the optimal gauges for FCIs with different forms of interaction, including a short-range interaction, the Coulomb interaction, and an interpolation between them, by applying the variational principle proposed by Zhang et al. [Phys. Rev. B 93, 165129 (2016)]. We find that the optimal gauge strongly depends on the form of interaction. It contradicts with the common belief that the wave function of FCI is not sensitive to the interaction. In comparing the optimal gauge with the previous gauges proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] and Wu et al. [Phys. Rev. B 86, 085129 (2012)], we find Wu et al.'s gauge is close to the optimal one when the interaction is a certain mixture of the Coulomb interaction and the short-range interaction, while Qi's gauge is qualitatively different from the optimal gauge in all the cases.
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.
We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models at $\ensuremath{\nu}=1/3$ filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than
0.99 in some models when the Hilbert space dimension is as large as $3\ifmmode\times\else\texttimes\fi{}{10}^{4}$ in each total momentum sector.
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.
Fractional Chern insulators have attracted broad interest as lattice analogs of fractional quantum Hall states without Landau levels. However, low-filling fractional Chern insulators are fragile because charge-ordered phases can compete strongly with the fractional topological liquid. Here, we propose a center-decorated kagome model, motivated by geometry-tunable artificial lattices, in which the center-site hopping
t2 provides a direct knob for the quantum geometry of an isolated
C=1 flat band. Here quantum geometry refers to the Berry curvature and Fubini--Study metric, which determine the form factors of interactions projected into the Chern band. Exact diagonalization shows that tuning
t2 away from the flatness-optimized kagome limit reduces the trace-condition deviation, suppresses competing charge order, and enhances the many-body stability at both
ν=1/3 and the more fragile
ν=1/5 filling. At
ν=1/5, this stability-enhanced window persists under nearby interaction profiles, including variations of the dominant third-neighbor repulsion and weak nearest-neighbor admixtures. Low-energy spectra, spectral flow, quasihole and entanglement counting, static structure factors, and the quantized total many-body Chern number
Ctot=1 consistently support Laughlin-like fractional Chern insulators. These results identify quantum-geometry engineering as a route to stabilizing dilute fractional Chern insulators beyond band-flatness optimization alone.