  As lattice analogs of fractional quantum Hall systems, fractional Chern
insulators (FCIs) exhibit enigmatic physical properties resulting from the
intricate interplay between single-body and many-body physics. In particular,
the design of ideal Chern band structures as hosts for FCIs necessitates the
joint consideration of energy, topology, and quantum geometry of the Chern
band. We devise an analytical optimization scheme that generates prototypical
FCI models satisfying the criteria of band flatness, homogeneous Berry
curvature, and isotropic quantum geometry. This is accomplished by adopting a
holomorphic coordinate representation of the Bloch states spanning the basis of
the Chern band. The resultant FCI models not only exhibit extensive tunability
despite having only few adjustable parameters, but are also amenable to
analytically controlled truncation schemes to accommodate any desired
constraint on the maximum hopping range or density-density interaction terms.
Together, our approach provides a starting point for engineering ideal FCI
models that are robust in the face of specifications imposed by analytical,
numerical, or experimental implementation.
