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

Mutual information and correlations across topological phase transitions in topologically ordered graphene zigzag nanoribbons