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

TL;DR

This paper develops a Green's function approach to study two-dimensional frustrated spin-1/2 Heisenberg lattices, improving accuracy over traditional methods and highlighting potential for large and complex magnetic systems.

Contribution

The paper introduces a self-consistent Green's function method for 2D frustrated spin systems, incorporating self-energy corrections for better accuracy over RPA approximations.

Findings

Self-energy corrections improve accuracy for scalar interactions.

Method performs well for large systems and long-range interactions.

Performance is less accurate for cross-product (antisymmetric) interactions.

Abstract

The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for 2-dimensional magnetic systems with frustrated spin-1/2 Heisenberg exchange coupling. Compared to 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 Green's function 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.