Two strongly bound fermion pairs in a one-dimensional trap: a composite-boson approach

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

Córdoba

Conferencia; XI Conference on Quantum Foundations: Contextuality, coherence and quantumness; 2022

Facultad de Matemática, Astronimía y Física

The ground state of a 1D system formed by two interacting fermionic pairs in a harmonic trap, with attractive contact interaction, was studied in the context of coboson formalism. The aim of this work was to analyze whether the coboson ansatz provides a good description of the system, at least in the strongly attractive regime in which it is supposed to be valid. Using tools from the coboson formalism based on the single-pair solutions, we were able to find a numerical approximation for the system valid for strongly attractive but finite interaction. The spatial and momentum correlations obtained, show that the coboson ansatz fails to describe the system even in the strongly attractive regime, since it cannot account for these correlations. In the infinite attraction limit the hard-core boson provides the exact solution for fermionic pairs in the trap, allowing us to compare our numerical results for finite interaction with the exact solution showing good agreement for sufficiently strong interaction values.