Quantum dynamics in 1D lattice models with synthetic horizons

Author:

Morice Corentin1,Chernyavsky Dmitry2,van Wezel Jasper1,van den Brink Jeroen324,Moghaddam Ali25

Affiliation:

1. Institute of Physics, University of Amsterdam

2. Leibniz Institute for Solid State and Materials Research

3. Dresden University of Technology

4. Würzburg-Dresden Cluster of Excellence

5. Institute for Advanced Studies in Basic Sciences

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.

Funder

Deutsche Forschungsgemeinschaft

Iran Science Elites Federation

Publisher

Stichting SciPost

Subject

General Computer Science

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