In the past decade, tremendous efforts have been made towards understanding fermionic symmetry-protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite-dimensional Hilbert space in general. In this Letter, we give a lattice model construction and classification for two-dimensional (2D) interacting electronic insulators. Based on the physical picture of $\mathrm{U}{\left(1\right)}_f$ charge decorations, we illustrate the key idea by considering the well-known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry $G_f=\mathrm{U}{\left(1\right)}_f{⋊}_{{\rho }_1,{\omega }_2}G$, where $\mathrm{U}{\left(1\right)}_f$ is the charge conservation symmetry and ${\rho }_1,{\omega }_2$ are additional data which fully characterize the group structure of $G_f$. Finally, we study more examples, including the full interacting classification of 2D crystalline topological insulators.

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• Symmetry protected topological states
• Topological insulators
• Topological materials