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 exactlyreduces to Dirac fields subjected to (1+1)-dimensional [(1+1)D] gravitational backgrounds, including (anti-)deSitter space-time. Wave packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integralst(x)∝xγwhenγ 1, signaling the formation of black hole event horizons. Forγ<1 instead the wave packets behave radically different and bounce off the horizon. We show that the eternalslowdown relates to a zero-energy spectral singularity of the lattice model and that the semiclassical wave packetstrajectories coincide with the geodesics on (1+1)D dilaton gravity, paving the way for new and experimentallyfeasible routes to mimic black hole horizons and realize (1+1)D space-times as they appear in certain gravitytheories.