Local characterization of 1d topologically ordered states

Abstract

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 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 local scale. Therefore our analysis can serve as as local experimental test for topological order.

7 pages, 11 figures. Minor corrections, reference added. Published version

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• Universal aspects in the behavior of the entanglement spectrum in one dimension: scaling transition at the factorization point and ordered entangled structures
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• One-way deficit and quantum phase transitions in $XY$ model and extended Ising model
• Non universality of entanglement convertibility
• Interplay of entanglement structures and stabilizer entropy in spin models
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• Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps
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• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• One-way deficit and quantum phase transitions in $XX$ Model