Synthetic Horizons and Thermalization in an Atomic Chain and its Relation to Quantum Hall Systems

We investigate the sine model, a one-dimensional tight-binding Hamiltonian featuring hoppings with a sinusoidal dependence on position, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, employing the exact transformation between this model and the Harper equation, which describes the eigenstates of a square lattice tight-binding model subjected to a perpendicular magnetic field, we find that analogous semi-classical horizons can emerge in a quantum Hall setup at half-filling for specific values of the magnetic flux. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of thermal states characterized by an Unruh temperature. Our numerical calculations of this temperature reveal a non-universal behavior, suggesting the involvement of physical mechanisms beyond a simple low-energy description.