Entanglement dynamics of delocalized interacting particles

Quantum entanglement in systems of identical particles is often obscured by the interplay between exchange-induced correlations and the operational framework used to define entanglement. To study the role of exchange statistics, we propose a scheme using two \textit{distinguishable} particles where an exchange symmetry is artificially engineered via a relative phase $\theta$ in the initial state. This approach allows continuous tuning from bosonic ($\theta = 0$) to fermionic ($\theta = \pi$) statistics. By monitoring the interplay between purity and coherence, we uncover distinct dynamical regimes dictated by the interaction strength $U$ and the phase $\theta$. For particles initially loaded in a bound state, strong $U$ suppresses coherence development by avoiding the scattering band, reducing the purity toward its minimum. For particles initially on neighboring sites, coherence grows linearly in time. While non-symmetric inputs feature a sharp purity reduction at intermediate $U$, due to the competition between bound and unbound states, symmetric initial conditions produce transient coherence bursts that significantly enhance the purity. More generally, tuning the phase $\theta$ reveals a high-purity region over a range of $\theta$ at intermediate interactions, with the purity collapsing to $1/2$ as $\theta$ approaches the fermionic limit. Our results show that the imposed statistics, or lack thereof, reshapes the entanglement dynamics and its response to the interaction $U$.