Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in the d=3 t-J model: Finite-temperature global phase diagrams from renormalization group theory

The renormalization-group theory of the d=3 t-J model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, further/first-neighbor interaction-strength ratios. With the inclusion of further-neighbor interactions, an extremely rich phase diagram structure is found and is explained by competing and frustrated interactions. In addition to the tau(tJ) phase seen in earlier studies of the nearest-neighbor d=3 t-J model, the tau(Hb) phase seen before in the d=3 Hubbard model appears both near and away from half filling.