Broken-symmetry fully self-consistent GW: analysis of spin contamination, extraction of effective magnetic Hamiltonians, and evaluation of Neel temperatures in solid antiferromagnets

Recently, we applied the thermodynamic Hellmann-Feynman theorem to fully self-consistent Green's function methods, derived two-particle density matrices for molecules, and analyzed electronic structure in terms of two-particle correlators. In this work, we extend this development to solids. Since the conventional measure of spin contamination based on 2> is not extensive, we propose two new extensive quantities, u> and u^k=0>, that are suitable for measuring spin contamination in solids. We show that unlike previous DFT estimates, the unrestricted GW in NiO and MnO is close to the ideal ferromagnetic and broken-symmetry solutions, making extraction of effective magnetic couplings simple and unambiguous, agreeing well with very few quantitative finite-cluster wave-function calculations for NiO. The constructed effective Hamiltonian H_eff can be extrapolated for the strongly correlated states and system sizes that cannot be easily captured by conventional calculations. For the description of macroscopic phenomena, such as phase transitions, a direct diagonalization of the extrapolated H_eff is not feasible. Instead, we apply a high-temperature expansion for the magnetic susceptibility and heat capacity to this extrapolated Hamiltonian. The radius of convergence of the obtained series determines the Neel temperature T_N. We show that the experimentally observed trend in Neel temperatures in transition metal compounds is reproduced by broken-symmetry self-consistent GW.