  We study XXZ Heisenberg models on frustrated triangular lattices wrapped
around a cylinder. In addition to having interesting magnetic phases, these
models are equivalent to Bose-Hubbard models that describe the physical problem
of adsorption of noble gases on the surface of carbon nanotubes. We find
analytical results for the possible magnetization plateau values as a function
of the wrapping vectors of the cylinder, which in general introduce extra
geometric frustration besides the one due to the underlying triangular lattice.
We show that for particular wrapping vectors $(N,0)$, which correspond to the
zig-zag nanotubes, there is a macroscopically degenerate ground state in the
classical Ising limit. The Hilbert space for the degenerate states can be
enumerated by a mapping first into a path in a square lattice wrapped around a
cylinder (a Bratteli diagram), and then to free fermions interacting with a
single ${\bf Z}_N$ degree of freedom. From this model we obtain the spectrum in
the anisotropic Heisenberg limit, showing that it is gapless. The continuum
limit is a $c=1$ conformal field theory with compactification radius $R=N$ set
by the physical tube radius. We show that the compactification radius
quantization is exact in the projective $J_\perp/J_z \ll 1$ limit, and that
higher order corrections reduce the value of $R$. The particular case of a
$(N=2,0)$ tube, which corresponds to a 2-leg ladder with cross links, is
studied separately and shown to be gapped because the fermion mapped problem
contains superconducting pairing terms.
