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arXiv · 0802.0447

String order and symmetries in quantum spin lattices

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

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D. Perez-Garcia, M. M. Wolf, M. Sanz, F. Verstraete, J. I. Cirac. 2008-02-04. String order and symmetries in quantum spin lattices. https://doi.org/10.1103/physrevlett.100.167202

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