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Characterizing topological order form a microscopic lattice Hamiltonian

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In this talk I will show how to obtain a detailed characterization of the emergent topological order starting from microscopic Hamiltonian on a two dimensional lattice. A key step is to obtain a tensor network representation for a complete set of ground states of the Hamiltonian, first on an infinite cylinder and then on a finite torus. As an application of the method I will study lattice Hamiltonians that give rise to selected anyon models, namely chiral semion, Ising as well as Z_3 and Z_5 models.