Friday, July 26, 2013

1307.6617 (Iman Marvian)

Symmetry Protected Topological Entanglement    [PDF]

Iman Marvian
We propose an order parameter for the Symmetry Protected Topological (SPT) phases which are protected under an Abelian on-site symmetry. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B, two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by the regions A and B and the boundaries of the system. In the case of 1-dimensional systems we prove that at the limit where the regions A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the non-trivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth local quantum circuits which respect the symmetry, suggesting that the SPT entanglement remains constant throughout a SPT phase in the higher dimensions as well. Finally, we discuss the relation between the SPT entanglement and the string order parameters.
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