  Advances with trapped ultracold atoms intensified interest in simulating
complex physical phenomena, including quantum magnetism and transitions from
itinerant to non-itinerant behavior. Here we show formation of
antiferromagnetic ground states of few ultracold fermionic atoms in single and
double well (DW) traps, through microscopic Hamiltonian exact diagonalization
for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells,
and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D,
nature. The spectra and spin-resolved conditional probabilities reveal for both
cases, under strong repulsion, atomic spatial localization at extemporaneously
created sites, forming quantum molecular magnetic structures with non-itinerant
character. These findings usher future theoretical and experimental
explorations into the highly-correlated behavior of ultracold
strongly-repelling fermionic atoms in higher dimensions, beyond the
fermionization physics that is strictly applicable only in the 1D case. The
results for four atoms are well described with finite Heisenberg spin-chain and
cluster models. The numerical simulations of three fermionic atoms in symmetric
double wells reveal the emergent appearance of coupled resonating 2D Heisenberg
clusters, whose emulation requires the use of a t-J-like model, akin to that
used in investigations of high T$_c$ superconductivity. The highly entangled
states discovered in the microscopic and model calculations of controllably
detuned, asymmetric, double wells suggest three-cold-atom DW quantum computing
qubits.
