Interplay of spin-orbit coupling and non-local correlations with the Two-Particle Self-Consistent method

We show in which way it is possible to include spin-orbit coupling (SOC) terms in the Two-Particle Self-Consistent method (TPSC). TPSC is a many-body method, valid for weak to intermediate interaction strength, which with moderate computational effort allows to investigate non-local correlation effects [Vilk, Tremblay J. Phys. I France, 7 11 (1997) 1309-1368]. Originally developed for single-band lattice models, in recent years TPSC was extended to the multi-orbital case [Zantout et al., Phys. Rev. Lett. 123, 256401 (2019), Zantout et al., Annalen der Physik 2000399 (2021)]. Inclusion of SOC into TPSC is desirable to study systems in which the effects of SOC cannot be neglected as e.g. in Sr2RuO4 [Phys. Rev. Lett. 101, 026406 (2008)]. However, including SOC into TPSC is not straightforward since TPSC in its original formulation relies on spin rotational symmetry, a symmetry which is explicitly broken by SOC terms. We present key ideas which make this nevertheless possible and discuss the effect spin-orbit coupling on the self-energy and spin and charge correlation functions of interacting model systems.