Synthetic gravitational horizons in low-dimensional quantum matter

TL;DR

This paper introduces lattice models that simulate (1+1)D gravitational backgrounds, demonstrating black hole horizon phenomena through wave-packet dynamics, and linking these to geodesics in dilaton gravity.

Contribution

It presents a class of lattice models that exactly mimic Dirac fields in (1+1)D gravitational spacetimes, including black hole horizons, with experimentally feasible setups.

Findings

Wave-packets slow down and form horizons for $eta extgreater= 1$

Wave-packets bounce off horizons for $eta extless 1$

Semiclassical trajectories match geodesics in (1+1)D dilaton gravity

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 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.