Statistics induced phase transitions in the extended bosonic anyon Hubbard model

We study a 1D extended Hubbard model of anyons with statistical exchange phases ranging from bosons to pseudo-fermions. The model can be realized in optical lattice experiments implementing occupation-dependent hopping amplitudes. We enforce a two-body hard-core constraint and numerically determine the full phase diagram including attractive on-site interactions. Surprisingly, the symmetry protected topological Haldane phase remains robust up to large statistical angles close to the pseudo-fermionic limit. However, for a critical angle the phase diagram qualitatively changes involving a dimer phase while the Haldane phase disappears. This behavior is analytically described by an adapted bosonization approach.