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

TL;DR

This study investigates the ground-state magnetization of a few ultra-cold fermions in one-dimensional traps, revealing how trap shape, interactions, and magnetic fields influence the system's magnetization phases.

Contribution

It introduces a method that treats spin as an active degree of freedom, allowing spontaneous magnetization without fixed spin projection assumptions.

Findings

Magnetization depends on trap shape, interactions, and magnetic field.

Certain magnetization values are inaccessible in the ground state for specific confinements.

The phase diagram of the system is mapped based on these parameters.

Abstract

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.