| Ideal wavefunctions such as the Laughlin wavefunction, as well as the corresponding trial Hamiltonians for which the former are exact ground states, have been vital to characterizing FQH phases. Adopting this concept to the lattice, we apply the Wannier function representation to develop a systematic pseudopotential formalism for fractional Chern insulators. The family of pseudopotential Hamiltonians is defined as the set of projectors onto asymptotic relative angular momentum components which forms an orthogonal basis of two-body Hamiltonians with magnetic translation symmetry. This approach serves both as an expansion tool for interactions and as a definition of positive semidefinite Hamiltonians for which the ideal fractional Chern insulator wavefunctions are exact nullspace modes. We discuss the effect of inhomogeneous Berry curvature which leads to components of the Hamiltonian that cannot be expanded into pseudopotentials, and elaborate on their role in determining low energy theories for fractional Chern insulators. Furthermore, we generalize our Chern pseudopotential approach to many-body interactions. |
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