  Electronic states at the ends of a narrow armchair nanoribbon give rise to a
pair of non-locally entangled spins. We propose two experiments to probe these
magnetic states, based on magnetometry and tunneling spectroscopy, in which
correlation effects lead to a striking, nonlinear response to external magnetic
fields. On the basis of low-energy theories that we derive here, it is
remarkably simple to assess these nonlinear signatures for magnetic edge
states. The effective theories are especially suitable in parameter regimes
where other methods such as quantum Monte-Carlo simulations are exceedingly
difficult due to exponentially small energy scales. The armchair ribbon setup
discussed here provides a promisingly well-controlled (both experimentally and
theoretically) environment for studying the principles behind edge magnetism in
graphene-based nano-structures.
