String order and symmetries in quantum spin lattices.
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.
Pérez-García
D
D
Departamento de Analisis Matematico, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Wolf
M M
MM
Sanz
M
M
Verstraete
F
F
Cirac
J I
JI