Ground-State Magnetization in Mixtures of a Few Ultra-Cold Fermions in One-Dimensional Traps

Ground-state properties of a few spin-$1/2$ ultra-cold fermions confined in a one-dimensional trap are studied by the exact diagonalization method. In contrast to previous studies, it is not assumed that the projection of a spin of individual particles is fixed. Therefore, the spin is treated as an additional degree of freedom and the global magnetization of the system is established spontaneously. Depending on the shape of the trap, inter-particle interactions, and an external magnetic field, the phase diagram of the system is determined. It is shown that, for particular confinements, some values of the magnetization cannot be reached by the ground-state of the system.Comment: This article belongs to the Special Issue "New Trends in Quantum Complex Matter

Mean-field approaches to the Bose-Hubbard model with three-body local interaction

The zero temperature properties of the generalized Bose-Hubbard model including three-body interactions are studied on a mean-field level. We obtain analytical results using the so-called perturbative mean-field method and more detailed numerical results using the Gutzwiller product state variational Ansatz. These two approaches yield equivalent results which compare well on a qualitative level with recent exact results obtained in the literature.Comment: Proceedings of the CEWQO 201