String Order and Symmetries in Quantum Spin Lattices

Author(s): D. Perez-Garcia, M. M. Wolf, M. Sanz, F. Verstraete, J. I. Cirac

Journal: Physical Review Letters

Volume: 100

Page(s): 167202

Year: 2008

DOI Number: 10.1103/PhysRevLett.100.167202

Link: Link to publication


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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