%0 Journal Article
%A Pérez García, David
%A Wolf, M.M.
%A Sanz, M.
%A Verstraete, F.
%A Cirac, J.I.
%T String order and symmetries in quantum spin lattices
%D 2008
%@ 0031-9007
%U https://hdl.handle.net/20.500.14352/50312
%X 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.
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