  Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties
of anyons in a one-dimensional lattice. To this end we map the hopping dynamics
of correlated anyons to an occupation-dependent hopping Bose-Hubbard model
using the fractional Jordan-Wigner transformation. In particular, we calculate
the quasi-momentum distribution of anyons, which interpolates between
Bose-Einstein and Fermi-Dirac statistics. Analytically, we apply a modified
Gutzwiller mean-field approach, which goes beyond a classical one by including
the influence of the fractional phase of anyons within the many-body
wavefunction. Numerically, we use the density-matrix renormalization group by
relying on the ansatz of matrix product states. As a result it turns out that
the anyonic quasi-momentum distribution reveals both a peak-shift and an
asymmetry which mainly originates from the nonlocal string property. In
addition, we determine the corresponding quasi-momentum distribution of the
Jordan-Wigner transformed bosons, where, in contrast to the hard-core case, we
also observe an asymmetry for the soft-core case, which strongly depends on the
particle number density.
