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String order and symmetries in quantum spin lattices

D. Perez-Garcia, M.M. Wolf, M. Sanz, F. Verstraete, J.I. Cirac

Phys. Rev. Lett. 100, 167202 **, (2008)

DOI: 10.1103/PhysRevLett.100.167202 Pfeil
*arXiv.org*: 0802.0447 Pfeil

Abstract: 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 to understand in a straightforward way many of the properties of string order parameters, like their robustness/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.