费米子-费米子相互作用驱动的二维倾斜半狄拉克半金属中的低能临界行为

Wen Liu, Wen-Hao Bian, Xiao-Zhuo Chu, Jing Wang
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摘要

我们采用重正化群方法,仔细研究了二维倾斜半狄拉克半金属在低能制度下由费米子-费米子相互作用诱导的临界行为。在纳入所有一回路修正之后,我们推导出了所有相关参数的耦合 RG 方程,并引入了两种不同的策略,分别命名为策略 I 和策略 II,以描述不同的情形。通过详细的数值分析,我们发现了低能极限的一些有趣行为。首先,我们注意到,在策略 I 中,费米子与费米子之间的相互作用要么消失,要么发散,这取决于倾斜参数和费米子耦合的初始值;而在策略 II 中,这些相互作用总是在某个临界能量尺度上发散,这与初始条件有关。接下来,策略 I 中的微结构参数 $\alpha$ 和费米子速度 $v_F$ 与策略 II 中的对应参数具有相似的行为。据观察,费米子与费米子之间的相互作用导致 $\alpha$ 增加,同时驱动 $v_F$ 减小。此外,在策略 I 中,系统既可以被高斯定点(GFP)吸引,也可以被某些相对定点(RFP)吸引,但在策略 II 中,系统在最低能量极限时总是流向 RFP。这些结果将为研究二维倾斜半狄拉克半金属和类似半金属中的可观测量和相位转换提供有益的启示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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