The self-energy-functional approach is a powerful many-body tool to investigate different broken symmetry phases of strongly correlated electron systems. We use the variational cluster perturbation theory (also called the variational cluster approximation) to investigate the interplay between the antiferromagnetism and d-wave superconductivity of k-(ET)2 X conductors. These compounds are described by the so-called dimer Hubbard model, with various values of the on-site repulsion U and diagonal hopping amplitude t'. At strong coupling, our zero-temperature calculations show a transition from Néel antiferromagnetism to a spin-liquid phase with no long range order, at around t' ~ 0.9. At lower values of U, we find d-wave superconductivity. Taking into account the point group symmetries of the lattice, we find a transition between n d x2-y2 and dxy pairing symmetries, the latter happening for smaller values of U.

Investigation of broken symmetry phases with long range order in strongly correlated electron systems is among subjects that have always been of interest to condensed matter scientists. In this paper we tried to study the existence of the 120 degrees magnetic spiral order, based on anisotropy in geometrically frustrated triangular lattices, using variational cluster approximation. We observed that by increasing the anisotropy in the system, the spiral order can be found for AWT IMAGE and for AWT IMAGE; however, it is limited by decreasing AWT IMAGE since antiferromagnetism is dominant for AWT IMAGE. Studying the Mott transition shows that a paramagnetic insulating phase, called quantum spin liquid, happens in the neighborhood of the spiral ordered phase.