Phase transitions in strongly correlated electronic systems

Abstract

We studied the some type of phase transitions in Strongly Correlated Electronic Systems. In particular we rigorously established some exact properties of a multi-orbital Hubbard model, here formulated to describe a nematic phase transition. In the first step, using Bogoliubov’s inequality, we rigorously showed that the multiorbital Hubbard model with narrow bands, eventually in the presence of the spin-orbit coupling, does not exhibit long-range nematic order, in the low dimensions. This result holds at any finite temperature for both repulsive and attractive on-site Coulomb interactions, with and without spin-orbit coupling. In the following step, using the reflection positivity method, we showed that this model supports a staggered nematic 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 lattice where the model is defined, the order may or not may exist. Indeed, in three dimensions the order may exist at finite temperature, and we get the condition for its existence finding out an upper bound for the critical temperature. On the other hand, for two dimensional lattices, the order may exist at least in the ground state, if the hopping amplitude is small enough. Furthermore, in the final step, we studied the symmetry properties of the non-degenerate Hubbard model with spin-orbit interactions of Rashba and Dresselhaus type. These interactions break the rotational symmetry in spin space, so that the magnetic order cannot be excluded by using the Bogoliubov inequality method. Nevertheless, we rigorously show that the existence of the magnetic long-range orders may be ruled out when the Rashba and Dresselhaus coupling constants are equal in modulus, whereas the -pairing can be always ruled out, regardless of the microscopic parameters of the model. These results are obtained by imposing locally the SU(2) gauge symmetry on the lattice, and rewriting the spin-orbit interactions in such a way that they are included in the path ordered of the gauge field on lattice. [edited by author]