Dirac fields in curved spacetime as Fermi-Hubbard model with non unitary tunnelings

TL;DR

This paper demonstrates how Dirac fields in curved spacetime can be modeled as a Fermi-Hubbard system with non-unitary tunnelings, enabling experimental simulation of quantum field effects in curved backgrounds.

Contribution

It provides a novel mapping between Dirac Hamiltonians in curved spacetime and non-unitary Fermi-Hubbard models, facilitating experimental realization with cold atoms.

Findings

Mapping of curved spacetime Dirac Hamiltonian to Fermi-Hubbard model

Explicit form of non-unitary tunneling matrices in terms of metric tensor

Qualitative agreement with particle pair creation in expanding universe

Abstract

In this article we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling matrices in terms of the metric tensor. The main motivation behind this exercise is the feasibility of such Hamiltonians by means of laser assisted tunnelings in cold atomic experiments. The mapping thus provide a physical interpretation of such Hamiltonians. We demonstrate the use of the mapping on the example of time dependent metric in 2+1 dimensions. Studying the spin dynamics, we find qualitative agreement with known theoretical predictions, namely the particle pair creation in expanding universe.