  To explore the static properties of the one-dimensional anyon-Hubbard model
for a mean density of one particle per site, we apply perturbation theory with
respect to the ratio between kinetic energy and interaction energy in the Mott
insulating phase. The strong-coupling results for the ground-state energy, the
single-particle excitation energies, and the momentum distribution functions up
to 6th order in hopping are benchmarked against the numerically exact
(infinite) density-matrix renormalization group technique. Since these analytic
expressions are valid for any fractional phase $\theta$ of anyons, they will be
of great value for a sufficiently reliable analysis of future experiments,
avoiding extensive and costly numerical simulations.
