Synthetic gravitational horizons in low-dimensional quantum matter

Abstract

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 [(1+1)D] gravitational backgrounds, including (anti-)de Sitter space-time. Wave packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integrals t(x)∝xγ when γ≥1, signaling the formation of black hole event horizons. For γ<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 space-times as they appear in certain gravity theories.