Single- and two-particle spectra of a single immobile impurity immersed in a fermionic bath can be computed exactly and are characterized by divergent power laws (edge singularities). Here we present the leading lattice correction to this canonical problem by embedding both impurity and bath fermions in bands with nonvanishing Bloch band geometry, with the impurity band being flat. By analyzing generic Feynman diagrams, we pinpoint how the band geometry reduces the effective interaction which enters the power laws; we find that for weak lattice effects or small Fermi momenta, the leading correction is proportional to the Fermi energy times the sum of the quantum metrics of the bands. When only the bath fermion geometry is important, the results can be extended to large Fermi momenta and strong lattice effects and cross-validated by analysis of $S$-matrix eigenvalues. We numerically illustrate our results on the Lieb lattice and draw connections to various spectroscopy experiments.

中文翻译：

---

相关平带的极化子光谱和边缘奇点

浸入费米子浴中的单一固定杂质的单粒子和双粒子光谱可以精确计算，并通过发散幂律（边缘奇点）来表征。在这里，我们通过将杂质和浴费米子嵌入具有非零布洛赫带几何形状的带中，并且杂质带是平坦的，提出了对这个典型问题的主要晶格校正。通过分析通用费曼图，我们查明能带几何形状如何减少进入幂律的有效相互作用；我们发现，对于弱晶格效应或小费米动量，主导修正与费米能量乘以能带量子度量之和成正比。当只有浴费米子几何结构很重要时，结果可以扩展到大费米动量和强晶格效应，并通过分析进行交叉验证$S$- 矩阵特征值。我们用数字说明了利布晶格的结果，并与各种光谱实验建立了联系。