Understanding Weakly Interacting van der Waals Fermi Systems via Renormalization Group Theory

Weak-coupling phenomena of the two-dimensional Hubbard model is gaining momentum as a new interesting research field due to its extraordinarily rich behavior as a function of the carrier density and model parameters. Salmhofer [Commun. Math. Phys. 194, 249 (1998);Phys. Rev. Lett. 87, 187004 (2001)] developed a new renormalization-group method for interacting Fermi systems and Metzner [Phys. Rev. B 61, 7364 (2000);Phys. Rev. Lett. 85, 5162 (2000)] implemented this renormalization group analysis of the two-dimensional Hubbard model. In this work, we demonstrate the spin-wave dependent susceptibility behavior of model graphene-phosphorene van der Waals heterostructure in the framework of renormalization group approach. We implement signlet vertex response function for the weakly interacting van der Waals Fermi system with nearest-neighbor hopping amplitudes [J. Phys.: Condens. Matter 33, 335604 (2021)]. This analytical approach is further correlated with ab initio simulation results and extended for spin-wave dependent susceptibility behavior with possible experimental protocols. We present the resulting compressibility and phase diagram in the vicinity of half-filling, and also results for the density dependence of the critical energy scale.