  An advanced cooling scheme, incorporating entropy engineering, is vital for
isolated artificial quantum systems designed to emulate the low-temperature
physics of strongly correlated electron systems (SCESs). This study
theoretically demonstrates a cooling method employing multi-component Fermi
gases with SU($\mathcal{N}$)-symmetric interactions, focusing on the case of
$^{173}$Yb atoms in a two-dimensional optical lattice. Adiabatically
introducing a nonuniform state-selective laser gives rise to two distinct
subsystems: a central low-temperature region, exclusively composed of two
specific spin components, acts as a quantum simulator for SCESs, while the
surrounding $\mathcal{N}$-component mixture retains a significant portion of
the entropy of the system. The SU($\mathcal{N}$)-symmetric interactions ensure
that the total particle numbers for each component become good quantum numbers,
creating a sharp boundary for the two-component region. The cooling efficiency
is assessed through extensive finite-temperature Lanczos calculations. The
results lay the foundation for quantum simulations of two-dimensional systems
of Hubbard or Heisenberg type, offering crucial insights into intriguing
low-temperature phenomena in condensed-matter physics.
