Phase diagram of the magnetic state obtained from a two-particle self-consistent analysis of the half-filled Hubbard model on a honeycomb lattice

Abstract

Motivated by the fascinating magnetic properties in the half-filled Hubbard model on a honeycomb lattice, we calculate the spin susceptibility and estimate the magnetic transition by applying the two-particle self-consistent (TPSC) method. The diagonalized spin-susceptibility matrix has its maximum at Q = 0, which indicates that an uniform magnetic order develops between the unit cells. The sign of the spin susceptibility between same sublattices is opposite to that between different sublattices. Therefore, an antiferromagnetic state develops in this system. We calculate the temperature dependence of the Stoner factor and estimate the critical temperature extrapolation. By applying the same analysis to several values of on-site interactions, we present the phase diagram of the magnetic state in the half-filled Hubbard model on a honeycomb lattice. Based on the phase diagram, the critical on-site interaction Uc/t above which magnetism occurs at the ground state can be estimated as being approximately 3.81.