Anomalous localization in spin-chain with tilted interactions

The localization properties of a disorder-free spin chain with inhomogeneous interactions are studied. In particular, we consider interaction strength growing linearly along the chain for systems with different interaction ranges. Using exact diagonalization we find the participation ratio of all eigenstates which allows us to quantify the localization volume in the Hilbert space. Surprisingly the localization volume changes nonmonotonically with the interaction range. The model for the infinite interaction range resembles the Schwinger model of lattice gauge theory in staggered formalism. The model studied may be implemented in state-of-the-art cold atomic devices and could reveal hidden features in disorder-free confinement phenomena.