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00925njm 22002777a 4500 dc Pérez García, David author Wolf, M.M. author Sanz, M. author Verstraete, F. author Cirac, J.I. author 2008-04-25 We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection is established, we provide a complete characterization of local symmetries in these states. The results allow us to understand in a straightforward way many of the properties of string order parameters, like their robustness or fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions. 0031-9007 10.1103/PhysRevLett.100.167202 https://hdl.handle.net/20.500.14352/50312 http://link.aps.org/doi/10.1103/PhysRevLett.100.167202 http://www.aps.org/ String order and symmetries in quantum spin lattices