We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized \emph{two-dimensional} projected Wannier functions of a Landau level.
@article{arxiv.1510.00524,
title = {Mapping a fractional quantum Hall state to a fractional Chern insulator},
author = {Yinhan Zhang and Junren Shi},
journal= {arXiv preprint arXiv:1510.00524},
year = {2016}
}