Bosonic behavior of interacting fermions in a strictly and non-strictly one-dimensional system

JIMÉNEZ, MARTÍN D.; CUESTAS, ELOISA; MAJTEY, ANA P.

Conferencia; X Conference on Quantum Fundations; 2021

We analyzed the bosonic behavior of a one-dimensional system formed by fermionic pairs with contact interaction at their ground state. We considered the cases where the constituents of the pair are impenetrable particles (strictly 1D), and the case where they can tunnel between them (non-strictly 1D). We then used two different representations for the single pair state, one of them equivalent to a system with two distinguishable fermions, and the other to a system of interacting identical fermions. From the single pair state, and using an ansatz of composite bosons, we studied some properties of the system when the number of pairs is increased and the interaction is varied over its entire range, and we have linked them directly with entanglement between the single pair components. For all the calculations the eigenvalues of reduced density matrix were required, in addition to an adequate entanglement definition in terms of these eigenvalues for each kind of system. The form of these eigenvalues near the very small entanglement regime leads in both cases to a behavior of the eigenstates of reduced density matrix occupation numbers when the number of pairs is increased which reveals that the particles do not fully fill the eigenstates with the greatest eigenvalue. At the extreme values of the interaction parameter the results also reveal interesting properties, such as fermionization phenomena in the strongly repulsive regime, and ideally bosonic behavior in a strongly attractive regime.