Crystallization in Topological Flat Bands in Thin Torus Limit

We study a crystallization on partially filled topological flat bands of honeycomb lattice in the thin torus limit. We identify the crystallization by looking at the pair correlation densities and determine the strength of the crystallization from their Fourier transform. We observed that the crystallization depends on the parity of the denominator of the filling factor. The crystallization is weakly affected by finite size effects and its strength increases with decrease of a particle density.