One-dimensional Bose-Fermi mixture under local and next-neighbor interactions.

We investigate a mixture composed of two-color fermions and scalar bosons in the hard-core limit, considering local interspecies and intraspecies interactions as well as the next-neighbor interactions between fermions or bosons. It is well known that the interplay between commensurability and local repulsive interactions generates diverse Mott insulator states in Bose-Fermi mixtures [PRA 100, 063620 (19); PRA 102, 033341 (2020); PRA 103, 023304 (2021)]. Also in the absence of bosons, the ground state of two-color fermions with local and next-neighbor interactions exhibit a rich phase diagram. Here, we explore the ground state of Bose-Fermi mixture considering local and next-neighbor couplings, finding that the mixed Mott insulator and the spin-selective one are strongly affect by the no local interactions.