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.
In this paper we propose an exactly soluble model in a two-dimensional honeycomb lattice, from which two phases are found. One is the usual Chern/topological insulating state and the other is an interesting
Z2 fractionalized Chern/topological insulator. While their bulk properties are similar, the edge states of physical electrons are quite different. The single electron excitation of the former shows a free particle like behavior while the latter one is gapped, which provides a definite signature to identify the fractionalized states. The transition between these two phases is found to fall into the three-dimensional Ising universal class. Significantly, near the quantum transition point the physical electron in the edge states shows strong Luttinger liquid behavior. An extension to the interesting case of the square lattice is also made. In addition, we also discuss some relationship between our exactly soluble model and various Hubbard-like models existing in the literature. The essential difference between the proposed
Z2 fractionalized Chern insulator and the hotly pursued fractional Chern insulator is also pointed out. The present work may be helpful for further study on the fractionalized insulating phase and related novel correlated quantum phases.