Metal–insulator transition in the antiferromagnetic state of the Hubbard model: analytical theory

In the framework of numerical calculations and analytical expansion in the transfer integral between the next-nearest neighbors t' and the direct antiferromagnetic (AFM) gap , the metal-insulator transition criterion is obtained, the Hartree-Fock and slave boson approaches being used. In the case of a square lattice, there is an interval of t' values, for which the metal-insulator transition is a first-order transition, which is due to the Van Hove singularity near the center of the band. For simple and body-centered cubic lattices, the transition from the insulator AFM state occurs to the phase of an AFM metal and is a second-order phase transition; it is followed by a transition to a paramagnetic metal. These results are modified when taking into account the intersite Heisenberg interaction which can induce first-order transitions. © Published under licence by IOP Publishing Ltd. Russian Academy of Sciences, RAS Government Council on Grants, Russian Federation: 02. We are grateful to M.A. Timirgazin for helpful discussions. The research was carried out within the Russia Federation state assignment (theme “Quantum” No. -18-118020190095-4), the project No. 18-2-2-11 by the Division of Physical Sciences and Ural Branch, Russian Academy of Sciences and partial support by Program 211 of the Government of the Russian Federation (Agreement 02.A03.21.0006).