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.
Departamento de Analisis Matematico, Universidad Complutense de Madrid, 28040 Madrid, Spain.
D
D
Pérez-García
M M
MM
Wolf
M
M
Sanz
F
F
Verstraete
J I
JI
Cirac