Nematic phase transition in a multi-orbital Hubbard model

By using the reflection positivity method, we rigorously establish some exact properties of a multi-orbital Hubbard model, here adopted to describe a nematic orbital phase transition. We show that, when the on-site intra-orbital Coulomb interaction is equal to the on-site inter-orbital Coulomb interaction, this model supports a staggered nematic orbital order if repulsive or attractive on-site inter-orbital and intra-orbital interactions and off-site repulsive inter-orbital interaction are considered. Depending on the dimensions of the bipartite lattice where the model is defined, we find that, at half-filling, the order may or may not exist. In particular, we prove that the order may exist, in two and three dimensions, at sufficiently low temperatures if the hopping amplitude is small enough.