We investigate the $2k_F$ density wave instability of non-Fermi-liquid states by combining exact diagonalization with renormalization group analysis. At the half-filled zeroth Landau level, we study the fate of the composite Fermi liquid in the presence of the mass anisotropy and mixed Landau level form factors. These two experimentally accessible knobs trigger a phase transition towards a unidirectional charge density wave state with a wave vector equal to $2k_F$ of the composite Fermi liquid. Based on exact diagonalization, we identify such a transition by examining both the energy spectra and the static structure factor of charge density-density correlations. Moreover, the renormalization group analysis reveals that gauge fluctuations render the non-Fermi-liquid state unstable against density wave orders, consistent with numerical observations. Possible experimental probes of the density wave instability are also discussed.

中文翻译：

---

复合费米液体的2kF密度波不稳定性

我们调查 $2{ķ}_F$非精确液态的密度波不稳定性，通过精确对角线化与重归一化组分析相结合。在半填充的零朗道能级下，我们研究了在存在质量各向异性和混合朗道能级形状因子的情况下复合费米液体的命运。这两个可通过实验访问的旋钮触发向单向电荷密度波状态的相变，其波矢量等于$2{ķ}_F$复合费米液体。基于精确的对角线化，我们通过检查能谱和电荷密度-密度相关性的静态结构因子来识别这种转变。此外，重归一化组分析显示，规范波动使非费米液态对密度波阶不稳定，这与数值观测结果一致。还讨论了密度波不稳定性的可能的实验探针。