Fusion rules from entanglement

Connections between 2D gapped quantum phases and the anyon fusion theory have been proven in various ways under different settings. In this work, we introduce a new framework connecting them by only assuming a conjectured form of entanglement area law for 2D gapped systems. We show that one can systematically define topological charges and fusion rules from the area law alone, in a well-defined way. We then derive the fusion rules of charges satisfy all the axioms required in the algebraic theory of anyons. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy, this term is shown to be equal to the logarithm of the total quantum dimension of the anyon theory we defined.