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We perform an exact diagonalization study of the topological order intopological flat band models through calculating entanglement entropy andspectra of low energy states. We identify multiple independent minimalentangled states, which form a set of orthogonal basis states for theground-state manifold. We extract the modular transformation matrices S (U)which contains the information of mutual (self) statistics, quantum dimensionsand fusion rule of quasi-particles. Moreover, we demonstrate that thesematrices are robust and universal in the whole topological phase againstdifferent perturbations until the quantum phase transition takes place.

Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands