Competing delocalisation and localisation induced by the dipolar tail in fragmented lattice gases

We investigate how the long-range tail of dipole-dipole interactions modifies the dynamics of strongly interacting hard-core bosons in a one-dimensional lattice. In the nearest-neighbour model, large interactions generate an emergent Hilbert-space fragmentation into manifolds labelled by the number of nearest-neighbour bonds N NN. The dipolar tail has a non-monotonic effect on this fragmented dynamics as the interaction-to-tunnelling ratio V/t is increased. At intermediate V/t, it enhances delocalisation relative to the nearest-neighbour model by reducing the energetic detuning between neighbouring N NN manifolds and sustaining their hybridisation by hopping. At larger V/t, the same tail lifts degeneracies within each manifold, beginning with the splitting associated with the next-nearest-neighbour bond number N NNN, and promotes intra-manifold localisation and Hilbert-space shattering. The competition between these two effects produces a crossover from a delocalising to a localising role of the dipolar tail, visible in the late-time spatial inhomogeneity. This crossover occurs for nearly all initial states considered and persists at different fillings. Transverse confinement strengthens the short-range part of the dipolar tail and shifts the crossover to lower V/t, bringing it into the regime relevant to current experiments with magnetic atoms and polar molecules.