  For most chiralities, semiconducting nanotubes display topologically
protected end states of multiple degeneracies. We demonstrate using density
matrix renormalization group based quantum chemistry tools that the presence of
Coulomb interactions induces the formation of robust end spins. These are the
close analogues of ferromagnetic edge states emerging in graphene nanoribbons.
The interaction between the two ends is sensitive to the length of the
nanotube, its dielectric constant, as well as the size of the end spins: for
$S=1/2$ end spins their interaction is antiferromagnetic, while for $S>1/2$ it
changes from antiferromagnetic to ferromagnetic as the nanotube length
increases. The interaction between end spins can be controlled by changing the
dielectric constant of the environment, thereby providing a possible platform
for two-spin quantum manipulations.
