We introduce a Bloch-like basis in a C-component lowest Landau level
fractional quantum Hall (FQH) effect, which entangles the real and internal
degrees of freedom and preserves an Nx x Ny full lattice translational
symmetry. We implement the Haldane pseudopotential Hamiltonians in this new
basis. Their ground states are the model FQH wave functions, and our Bloch
basis allows for a mutatis mutandis transcription of these model wave functions
to the fractional Chern insulator of arbitrary Chern number C, obtaining wave
functions different from all previous proposals. For C > 1, our wave functions
are related to color-dependent magnetic-flux inserted versions of Halperin and
non-Abelian color-singlet states. We then provide large-size numerical results
for both the C = 1 and C = 3 cases. This new approach leads to improved
overlaps compared to previous proposals. We also discuss the adiabatic
continuation from the fractional Chern insulator to the FQH in our Bloch basis,
both from the energy and the entanglement spectrum perspectives.Comment: 6+epsilon pages, 2 figures. Published version. Added a discussion of
the emergent particle-hole symmetry in a Chern ban
