Simulation of classical Ising-like magnetism with a Mott insulator of paired atoms

Quantum simulation of the XXZ model with a two-component Bose or Fermi Hubbard model based on a Mott insulator background has been widely used in the investigations of quantum magnetism with ultracold neutral atoms. In most cases, the diagonal spin-spin interaction is always accompanied by a large spin-exchange interaction which hinders the formation of long-range magnetic order at low temperature. Here we show that the spin-exchange interaction can be strongly reduced in a Mott insulator of paired atoms, while the diagonal spin-spin interaction remains unaffected. Thus, the effective magnetic model is quite close to an exact classical Ising model in the textbook. And we analysed an experimentally achievable three-component Fermi-Hubbard model of $\mathrm{{}^{6}Li}$ with two hyperfine levels of atoms paired in the lattice. We find the long-range antiferromagnetic order of such a three-component Fermi-Hubbard model can be much stronger than that of a typical two-component Fermi-Hubbard model at low temperature. And we discussed the possiblity of simulating an exact two-dimensional ferromagnetic Ising model in a Mott insulator of paired bosonic atoms. Our results may be useful for experimental investigation of the long-range Ising-like magnetism with ultracold neutral atoms under thermal equilibrium.