Low-energy critical behavior in two-dimensional tilted semi-Dirac semimetals driven by fermion-fermion interactions

Employing the renormalization group approach, we carefully investigate the critical behavior of two-dimensional tilted semi-Dirac semimetals induced by the fermion-fermion interactions in the low-energy regime. After incorporating all one-loop corrections, we derive the coupled RG equations of all related parameters and introduce two distinct strategies, named as Strategy I and Strategy II, to describe different scenarios. A detailed numerical analysis yields several interesting behavior in the low-energy limit. At first, we notice that the fermion-fermion interactions either vanish or diverge in the Strategy I, depending on the initial values of the tilting parameter and the fermionic couplings, whereas these interactions in the Strategy II always diverge at a certain critical energy scale, which is associated with the initial conditions. Next, the microstructural parameter $\alpha$ and the fermion velocity $v_F$ in the Strategy I share the similar behavior with their Strategy II counterparts. It is observed that fermion-fermion interactions lead to an increase in $\alpha$ while driving a decrease in $v_F$. Furthermore, the system can either be attracted by the Gaussian fixed point (GFP) or certain relatively fixed point (RFP) in the Strategy I. However, it always flow towards the RFP in the Strategy II at the lowest-energy limit. These results would provide helpful insights into the studies on observable quantities and phase transitions in the two-dimensional tilted semi-Dirac semimetals and the analogous semimetals.