Hilbert space fragmentation and interaction-induced localization in the extended Fermi-Hubbard model

We study Hilbert space fragmentation in the extended Fermi-Hubbard model with nearest-and next-nearest-neighbor interactions. Using a generalized spin/mover picture and saddle point methods, we derive lower bounds for the scaling of the number of frozen states and for the size of the largest block preserved under the dynamics. We find fragmentation for strong nearest-and next-nearest-neighbor repulsions as well as for the combined case. Our results suggest that the involvement of next-nearest-neighbor repulsions leads to an increased tendency for localization. We then model the dynamics for larger systems using Markov simulations to test these findings and unveil in which interaction regimes the dynamics becomes spatially localized. In particular, we show that for strong nearest-and next-nearest-neighbor interactions random initial states will localize provided that the density of initial movers is sufficiently low.