Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps

The occupancies and entropic entanglement measures for the ground state of two particles in a two-dimensional harmonic anisotropic trap are studied. We implement a method to study the large interaction strength limit for different short- and long-range interaction potentials that allows to obtain the exact entanglement spectrum and several entropies. We show that for long-range interactions, the von Neumann, min-entropy and the family of R\'enyi entropies remain finite for the anisotropic traps and diverge logarithmically for the isotropic traps. In the short-range interaction case the entanglement measures diverge for any anisotropic parameter due to the divergence of uncertainty in the momentum since for short-range interactions the relative position width vanishes. We also show that when the reduced density matrix has finite support the R\'enyi entropies present a non-analytical behaviour.