  Quantum simulators of lattice gauge theories involve dynamics of typically
short-ranged interacting particles and dynamical fields. Elimination of the
latter via Gauss law leads to infinite range interactions as exemplified by the
Schwinger model in a staggered formalism. This motivates the study of
long-range interactions, not necessarily diminishing with the distance. Here we
consider localization properties of a spin chain with interaction strength
growing linearly along the chain as for the Schwinger model. We generalize the
problem to models with different interaction ranges. Using exact
diagonalization we find the participation ratio of all eigenstates, which
allows us to quantify the localization volume in Hilbert space. Surprisingly,
the localization volume changes nonmonotonically with the interaction range.
Our study is relevant for quantum simulators of lattice gauge theories
implemented in state-of-the-art cold atom/ion devices, and it could help to
reveal hidden features in disorder-free confinement phenomena in long-range
interacting systems.
