Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines' chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.

Automated summary

In graphene, different chirality carbon lines entangle with each other in both the topologically ordered phase and crossover phases, with the entanglement increasing as more carbon lines are grouped together. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.