Quantum Phase Transitions in a Multi-orbital Hubbard Model with Spin-Orbit Coupling

We used the density matrix renormalization group technique to perform a detailed study of the effect of spin-orbit coupling on a three-orbital Hubbard model in one dimension [1]. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard U and spin-orbit coupling λ, at zero temperature for n=4 [2]. We also present the doping and spin-orbit coupling λ phase diagram, for intermediate and strong Hubbard U [3]. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing λ at intermediate U. In the strong U coupling limit, we find a nonmagnetic insulator with an effective angular momentum〈(Jeff)²〉≠0 near the excitonic phase, smoothly connected to the 〈(Jeff)²〉= 0 regime. In the same model we also found a novel and robust excitonic insulator phase with Block spin ordering, at various dopings and in both the intermediate and strong coupling region.
[1] J. Rincon et. al. Phys. Rev. Lett. 112, 106405 (2014)
[2] N. Kaushal et. al. Phys. Rev. B 96, 155111(2017)
[3] N. Kaushal et. al. unpublished