Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems

Abstract

We investigate the sine model, a one-dimensional tight-binding Hamiltonian with position-dependent sinusoidal hopping, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, using the exact transformation between this model and the Harper equation, we find that analogous semiclassical horizons can emerge in a quantum Hall setup within the Harper-equation representation and at half-filling for specific values of the magnetic flux. The Harper equation describes the eigenstates of a square-lattice tight-binding model subjected to a perpendicular magnetic field, as a family of one-dimensional problems parametrized by a conserved transverse quasi-momentum. We demonstrate the correspondence between the sine and Harper models by comparing their semiclassical phase-space portraits and by numerically studying wave-packet dynamics in both models. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of states with an effective thermal Fermi-Dirac distribution characterized by a corresponding Unruh temperature. Our numerical calculations reveal a non-universal behavior of this temperature, suggesting the involvement of mechanisms beyond a simple low-energy description.