  Recently, it was discussed that the $\nu=1/3$ fractional quantum Hall state
can be expressed by a one-dimensional lattice model with an exact matrix-prduct
ground state, when toroidal boundary conditions are assumed for a narrow strip
[Phys. Rev. Lett. {\bf 109} (2012) 016401]. In this article, we discuss how the
excitation spectra of this system are calculated analytically based on the
matrix-product formalism. We introduce variational wave functions for various
momenta and optimize them. The obtained spectra of the charge neutral
excitations show the magneto-roton behavior.
