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We computed the phase diagram of the zigzag graphene nanoribbons as afunction of on-site repulsion, doping, and disorder strength. The topologicallyordered phase undergoes topological phase transitions into crossover phases,which are new disordered phases with a nonuniversal topological entanglemententropy with significant variance. The topological order is destroyed bycompetition between localization effects and on-site repulsion. We found thatstrong on-site repulsion and/or doping weakens the nonlocal correlationsbetween the opposite zigzag edges. In one of the crossover phases, both$\frac{e^-}{2}$ fractional charges and spin-charge separation were absent;however, charge-transfer correlations between the zigzag edges were possible.Another crossover phase contains $\frac{e^-}{2}$ fractional charges, but nocharge transfer correlations. In low-doped zigzag ribbons the interplay betweenelectron localization and on-site repulsion contributes to the spatialseparation of quasi-degenerate gap-edge states and protects the chargefractionalization against quantum fluctuations. In all these effects, mixedchiral gap-edge states play an important role. The properties of nontopologicalstrongly disordered and strongly repulsive phases are also observed. Each phaseof the phase diagram has a different zigzag-edge structure.

Phase Diagram and Crossover Phases of Topologically Ordered Graphene Zigzag Nanoribbons: Role of Localization Effects