We computed the phase diagram of the zigzag graphene nanoribbons as a
function of on-site repulsion, doping, and disorder strength. The topologically
ordered phase undergoes topological phase transitions into crossover phases,
which are new disordered phases with a nonuniversal topological entanglement
entropy with significant variance. The topological order is destroyed by
competition between localization effects and on-site repulsion. We found that
strong on-site repulsion and/or doping weakens the nonlocal correlations
between the opposite zigzag edges. In one of the crossover phases, both
2eββ fractional charges and spin-charge separation were absent;
however, charge-transfer correlations between the zigzag edges were possible.
Another crossover phase contains 2eββ fractional charges, but no
charge transfer correlations. In low-doped zigzag ribbons the interplay between
electron localization and on-site repulsion contributes to the spatial
separation of quasi-degenerate gap-edge states and protects the charge
fractionalization against quantum fluctuations. In all these effects, mixed
chiral gap-edge states play an important role. The properties of nontopological
strongly disordered and strongly repulsive phases are also observed. Each phase
of the phase diagram has a different zigzag-edge structure