  We demonstrate numerically the existence of a nontrivial topological Haldane
phase for the one-dimensional extended ($U$-$V$) Hubbard model with a mean
density of one particle per site, not only for bosons but also for anyons,
despite a broken reflection parity symmetry. The Haldane insulator, surrounded
by superfluid, Mott insulator and density-wave phases in the $V$-$U$ parameter
plane, is protected by combined (modified) spatial-inversion and time-reversal
symmetries, which is verified within our matrix-product-state based infinite
density-matrix renormalization group scheme by analyzing generalized transfer
matrices. With regard to an experimental verification of the anyonic Haldane
insulator state the calculated asymmetry of the dynamical density structure
factor should be of particular importance.
