Abelian fractional Chern insulators have been previously investigated in hyperbolic kagome lattices with constant negative curvature, in which the geometric degree of freedom has been revealed. In this work, we study the $\nu =1$ non-Abelian fractional Chern insulator (FCI) with three-body hard-core bosons loaded into a topological flat band (TFB) model constructed in the hyperbolic analog of kagome lattice. Convincing numerical evidence is found for this non-Abelian FCI state, which is the Moore-Read-like ground state with clear edge excitation spectra. We also construct the trial wave function for this non-Abelian FCI based on the generalized Pauli principle, the Jack polynomials for the Moore-Read state, and single-particle states of the hyperbolic TFB model. A high value of overlap between the trial wave function and the exact diagonalization results demonstrates the existence of a hyperbolic non-Abelian FCI state. The inherent geometry of the hyperbolic non-Abelian FCI state is revealed as well.

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• Chern insulators
• Flat bands
• Fractional quantum Hall effect
• Strongly correlated systems
• Exact diagonalization
• Trial wave functions