Hawking radiation on the lattice from Floquet and local Hamiltonian quench dynamics

TL;DR

This paper constructs two lattice models of free fermions that demonstrate Hawking radiation via quench dynamics, showing how lattice discretization and mode scattering produce Hawking pairs consistent with quantum field theory predictions.

Contribution

The paper introduces two novel lattice models with quench dynamics that simulate Hawking radiation, highlighting the role of lattice modes as a reservoir for Hawking pairs.

Findings

Hawking spectrum matches Fermi-Dirac predictions up to the inverse lattice spacing.

Fermions scatter from the horizon region, either outside or inside, depending on the model.

Lattice discretization modes are crucial for the Hawking pair creation process.

Abstract

We construct two free fermion lattice models exhibiting Hawking pair creation. Specifically, we consider the simplest case of a d=1+1 massless Dirac fermion, for which the Hawking effect can be understood in terms of a quench of the uniform vacuum state with a non-uniform Hamiltonian that interfaces modes with opposite chirality. For both our models we find that additional modes arising from the lattice discretization play a crucial role, as they provide the bulk reservoir for the Hawking radiation: the Hawking pairs emerge from fermions deep inside the Fermi sea scattering off the effective black hole horizon. Our first model combines local hopping dynamics with a translation over one lattice site, and we find the resulting Floquet dynamics to realize a causal horizon, with fermions scattering from the region outside the horizon. For our second model, which relies on a purely local hopping Hamiltonian, we find the fermions to scatter from the inside. In both cases, for Hawking temperatures up to the inverse lattice spacing we numerically find the resulting Hawking spectrum to be in perfect agreement with the Fermi-Dirac quantum field theory prediction.