Synthetic gravitational horizons in low-dimensional quantum matter

We propose a class of lattice models realizable in a wide range of setups whose low-energy dynamics exactly reduces to Dirac fields subjected to (1+1)-dimensional gravitational backgrounds, including (anti-)de Sitter spacetime. Wave-packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integrals $t(x)\propto x^\gamma$ when $\gamma\geq 1$, signalling the formation of black hole event horizons. For $\gamma< 1$ instead the wave-packets behave radically different and bounce off the horizon. We show that the eternal slowdown relates to a zero-energy spectral singularity of the lattice model and that the semiclassical wave packets trajectories coincide with the geodesics on (1+1)D dilaton gravity, paving the way for new and experimentally feasible routes to mimic black hole horizons and realize (1+1)D spacetimes as they appear in certain gravity theories.