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

Cooling Fermions in an Optical Lattice by Adiabatic Demagnetization