Local characterization of 1d topologically ordered states

TL;DR

This paper demonstrates that ground states of 1d symmetry protected topological phases cannot be transformed into each other via LOCC, providing a local entanglement-based method to identify topological order.

Contribution

It introduces a local characterization method for 1d topologically ordered states based on entanglement properties, applicable to physical models like the Cluster-Ising and Haldane phases.

Findings

Ground states in the topological phase are LOCC-inaccessible.

Entanglement spectrum and Renyi entropies reveal topological distinctions.

Method offers a local experimental test for symmetry-protected topological order.

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.