L\'evy-Leblond fermions on the wormhole

Understand

We propose a simple model of entanglement generated by geometry, studying non-relativistic massive L\'evy-Leblond fermions in the $1+2$ geometry of a Bronnikov-Ellis wormhole.

• The model is equivalent to that of relativistic massless Dirac fermions in $1+3$ dimensions, where one spatial direction is flat.
• The effect of the wormhole is to generate quantum states that, far from the throat, are approximated by entangled particles on two flat, separated spacetime regions.
• An appealing feature of the model is that it has a condensed matter analogue, the regime of intermediate energies for two planes of bilayer graphene linked by a bilayer carbon nanotube.