Green's function method for the two-dimensional frustrated spin-1/2 Heisenberg magnetic lattice

The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function (GF) method is used to calculate ground state spin patterns and magnetic structure factors for two-dimensional magnetic systems with frustrated spin-1/2 Heisenberg exchange coupling. Compared with random phase approximation treatments, the inclusion of a self-energy correction improves the accuracy in the case of scalar product interactions, as shown by comparisons between our method and exact benchmarks in homogeneous and inhomogeneous finite systems. We also find that, for cross-product interactions (e.g., antisymmetric exchange), the method does not perform equally well, and an inclusion of higher corrections is in order. Aside from indications for future work, our results clearly indicate that the GF method in the form proposed here already shows potential advantages in the description of systems with a large number of atoms as well as long-range interactions.