Statistically induced phase transition in the extended Anyon-Hubbard model

We investigate the impact of non-trivial exchange statistics on bosonic SPT (Symmetry protected Topological) phases in one-dimensional optical lattices. As the underlying model we study the anyonic version of the extended Bose-Hubbard Hamiltonian with a generalized Pauli principle, restricting the maximal occupation up to two particles per site. Combining numerical DMRG techniques and a Gutzwiller Mean-Field treatment, we present the phase diagram of the system for different values of the statistical parameter. Additionally we employed bosonization to derive a low-energy field theory in order to describe the universal behavior of the system near the critical points, and analyze the mechanism behind statistically induced phase transitions present in the system.