Characteristic features of strong correlation: lessons from a 3-fermion one-dimensional harmonic trap

Many quantum phenomena responsible for key applications in material science and quantum chemistry arise in the strongly correlated regime. This is at the same time, a costly regime for computer simulations. In the limit of strong correlation analytic solutions exist, but as we move away from this limit numerical simulation are needed, and accurate quantum solutions do not scale well with the number of interacting particles. In this work we propose to use few-particle harmonic traps in combination with twisted light as a quantum emulator to investigate the transition into a strongly-correlated regime. Using both analytic derivations and numerical simulations we generalize previous findings on 2 Coulomb interacting fermions trapped in a one-dimensional harmonic trap to the case of 3 fermions. The 4 signatures of strong correlation we have identified in the one-dimensional harmonic trap are: (i) the ground state density is highly localized around N equilibrium positions, where N is the number of particles, (ii) the symmetric and antisymmetric ground state wavefunctions become degenerate, (iii) the von Neumann entropy grows, (iv) the energy spectrum is fully characterized by N normal modes or less. Our findings describe the low-energy behavior of electrons in quantum wires and ions in Paul traps. Similar features have also been reported for cold atoms in optical lattices.