标题： 二维和一维临界费米面的Migdal-Eliashberg理论是否稳定？ 显示英文标题

标题： Is the Migdal-Eliashberg Theory for 2+1D Critical Fermi Surface Stable?

摘要： 我们诊断了二维情况下费米面与无能隙玻色子耦合的Migdal-Eliashberg理论的稳定性。 我们提供了一种方案来对角化Bethe-Salpeter阶梯，当由玻色子介导的小角度散射起主导作用时。 我们发现大量软模对应于费米面的形状波动，并且这些形状变形在费米面上遵循类似于扩散的动力学。 出乎意料的是，凸起的费米面的奇宇称变形在Ising-向列量子临界点的非费米液体区域附近变得不稳定，我们的发现呼吁重新审视Migdal-Eliashberg框架。 Bethe-Salpeter本征值在输运中的含义将在后续论文[H.Guo, arXiv:2311.03458]中讨论。 显示英文摘要

摘要： We diagnose the stability of the Migdal-Eliashberg theory for a Fermi surface coupled to a gapless boson in 2+1 dimensions. We provide a scheme for diagonalizing the Bethe-Salpeter ladder when small-angle scattering mediated by the boson plays a dominant role. We found a large number of soft modes which correspond to shape fluctuations of the Fermi surface, and these shape deformations follow a diffusion-like dynamics on the Fermi surface. Surprisingly, the odd-parity deformations of a convex Fermi surface becomes unstable near the non-Fermi liquid regime of the Ising-Nematic quantum critical point and our finding calls for revisit of the Migdal-Eliashberg framework. The implication of the Bethe-Salpeter eigenvalues in transport will be discussed in the companion paper [H.Guo,arXiv:2311.03458].