Quantum dynamics in 1D lattice models with synthetic horizons

TL;DR

This paper explores quantum wave dynamics in 1D lattice models that simulate curved spacetime, revealing horizon-like behavior, wave packet slowdown, and eigenstate localization, supported by semiclassical analysis.

Contribution

It introduces a class of 1D lattice models with variable hopping that mimic black hole horizons and analyzes their wave dynamics and eigenstate localization.

Findings

Zero-energy wave packets slow down near the horizon

Non-zero energy wave packets bounce back before reaching the horizon

Eigenstates exhibit power-law localization with exponential suppression regions

Abstract

We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.