  We study the electronic correlation effects in armchair graphene nanoribbons
that have been recently proposed to be the building blocks of spin qubits. The
armchair edges give rise to peculiar quantum interferences and lead to quenched
kinetic energy of the itinerant carriers at appropriate doping level. This is a
beautiful one-dimensional analogy of the Landau-level formation in two
dimensions except the magnetic field is not needed here. Combining the
techniques of effective field theory and variational wave function approach, we
found that the ground state exhibits a new type of flat-band ferromagnetism
that hasn't been found before. At the end, we address practical issues about
realization of this novel magnetic state in experiments.
