Jian Cui, Luigi Amico, Heng Fan, Mile Gu, Alioscia Hamma, Vlatko Vedral
We consider 1d Hamiltonian systems whose ground states {display symmetry protected topological order}. We show that ground states within the topological phase cannot be connected {with} each other through LOCC between a bipartition of the system. Our claim is demonstrated by analyzing the eigenvalues of reduced density matrix (which is one to one corresponding to the entanglement spectrum) and Renyi entropies of different physical systems providing examples for symmetry protected topological phases. Specifically, we consider spin-1/2 Cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for simmetry-protected topological order, that holds true even at the system's {\it local scale}. Therefore our analysis can serve as as local experimental test for topological order.
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http://arxiv.org/abs/1304.2279
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