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

On the geometrical description of fractional Chern insulators based on static structure factor calculations