  We study the static structure factor of the fractional Chern insulator
Laughlin-like state and provide analytical forms for this quantity in the
long-distance limit. In the course of this we identify averaged over Brillouin
zone Fubini Study metric as the relevant metric in the long-distance limit. We
discuss under which conditions the static structure factor will assume the
usual behavior of Laughlin-like fractional quantum Hall system i.e. the
scenario of Girvin, MacDonald, and Platzman [Phys. Rev. B 33, 2481 (1986)]. We
study the influence of the departure of the averaged over Brillouin zone Fubini
Study metric from its fractional quantum Hall value which appears in the
long-distance analysis as an effective change of the filling factor. According
to our exact diagonalization results on the Haldane model and analytical
considerations we find persistence of fractional Chern insulator state even in
this region of the parameter space.
