Schuch, NorbertPérez García, DavidCirac, Ignacio2023-06-202023-06-2020100003-491610.1016/j.aop.2010.05.008https://hdl.handle.net/20.500.14352/41900We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenerate ground states and to characterize the ground state subspace. Subsequently, we apply our framework to show how the topological properties of these ground states can be explained solely from the symmetry: We prove that ground states are locally indistinguishable and can be transformed into each other by acting on a restricted region, we explain the origin of the topological entropy, and we discuss how to renormalize these states based on their symmetries. Finally, we show how the anyonic character of excitations can be understood as a consequence of the underlying symmetries.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0003491610000990open access51-73Matrix Product StatesProjected Entangled Pair States (PEPS)Tensor network statesTopological statesQuantum double modelsToric code stateAnyonsExactly solvable modelsFísica matemáticaTeoría cuánticaQuantum PhysicsMathematical PhysicsFísica matemáticaTeoría de los quanta2210.23 Teoría Cuántica