  The Fermi-Hubbard model describes ultracold fermions in an optical lattice
and exhibits antiferromagnetic long-ranged order below the N\'{e}el
temperature. However, reaching this temperature in the lab has remained an
elusive goal. In other atomic systems, such as trapped ions, low temperatures
have been successfully obtained by adiabatic demagnetization, in which a strong
effective magnetic field is applied to a spin-polarized system, and the
magnetic field is adiabatically reduced to zero. Unfortunately, applying this
approach to the Fermi-Hubbard model encounters a fundamental obstacle: the
$SU(2)$ symmetry introduces many level crossings that prevent the system from
reaching the ground state, even in principle. However, by breaking the $SU(2)$
symmetry with a spin-dependent tunneling, we show that adiabatic
demagnetization can achieve low temperature states. Using density matrix
renormalization group (DMRG) calculations in one dimension, we numerically find
that demagnetization protocols successfully reach low temperature states of a
spin-anisotropic Hubbard model, and we discuss how to optimize this protocol
for experimental viability. By subsequently ramping spin-dependent tunnelings
to spin-independent tunnelings, we expect that our protocol can be employed to
produce low-temperature states of the Fermi-Hubbard Model.
