Theory of Antiferromagnetic Mott States in the Hubbard Model

This work presents an analytical framework for antiferromagnetic Mott insulating states in the Hubbard model. We first derive an analytical solution for the single-particle Green's functions in the atomic limit. With a second-order perturbation theory, we compute the perturbation to the ground state energy and prove that the ground state is antiferromagnetically ordered. Then we derive an analytical solution for single-particle Green's functions in the presence of the hopping term for the Neel state. With the analytical solution, we compute and explain various properties of AFM Mott insulators observed both experimentally and numerically: i) magnetic blueshift of the Mott gap; ii) ARPES data on parental compounds of cuprate high Tc superconductors. This work not only enhances our understanding of electronic properties in AFM Mott states but also provides a solid foundation for future investigations of the doped AFM Mott insulators, which is believed to be the key to the mechanism of cuprates high-Tc superconductivity.