Coulomb and exchange interaction effects on the exact two-electron dynamics in the Hong-Ou-Mandel interferometer based on Hall edge states

The electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime is an ideal system to probe
the building up of quantum correlations between charge carriers and it has been proposed as a viable platform for
quantum computing gates. Using a parallel implementation of the split-step Fourier method, we simulated the
antibunching of two interacting fermionic wave packets impinging on a quantum point contact. Numerical results
of the exact approach are compared with a simplified theoretical model based on one-dimensional scattering
formalism. We show that, for strongly localized wave packets in a full-scale geometry, the Coulomb repulsion
dominates over the exchange energy, this effect being strongly dependent on the energy broadening of the
particles. We define analytically the spatial entanglement between the two regions of the quantum point contact,
and obtain quantitatively its entanglement-generation capabilities.