  Understanding the behavior of quantum systems subject to magnetic fields is
of fundamental importance and underpins quantum technologies. However, modeling
these systems is a complex task, because of many-body interactions and because
many-body approaches such as density functional theory get complicated by the
presence of a vector potential into the system Hamiltonian. We use the metric
space approach to quantum mechanics to study the effects of varying the
magnetic vector potential on quantum systems. The application of this technique
to model systems in the ground state provides insight into the fundamental
mapping at the core of current density functional theory, which relates the
many-body wavefunction, particle density and paramagnetic current density. We
show that the role of the paramagnetic current density in this relationship
becomes crucial when considering states with different magnetic quantum
numbers, $m$. Additionally, varying the magnetic field uncovers a richer
complexity for the "band structure" present in ground state metric spaces, as
compared to previous studies varying scalar potentials. The robust nature of
the metric space approach is strengthened by demonstrating the gauge invariance
of the related metric for the paramagnetic current density. We go beyond ground
state properties and apply this approach to excited states. The results suggest
that, under specific conditions, a universal behavior may exist for the
relationships between the physical quantities defining the system.
