The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for \(\sqrt{3}\times \sqrt{3}\) CDW order at an average electron filling of 〈n〉 = 2/3 per site, with an ordering wavevector at the K-points of the Brillouin zone. We estimate a phase transition occurring at T_c ≈ t/18, where t is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures T ≥ t/20.

Holstein 模型是对电子-声子相互作用的范式描述，其中电子耦合到局部无色散声子模式，与动量无关。该模型已被证明具有多种有序基态，例如电荷密度波 (CDW) 阶和多种几何形状的超导性，包括方形、蜂窝和 Lieb 晶格。在这项工作中，我们使用最近开发的混合蒙特卡罗模拟方法研究了 kagome 晶格上 Holstein 模型中的 CDW 形成。我们提供了\(\sqrt{3}\times \sqrt{3}\) CDW 阶的证据，每个位点的平均电子填充 < n > = 2/3，在布里渊的K点处有一个有序波矢量区。我们估计发生在T 的相变_c  ≈  t /18，其中t是最近邻跳跃参数。我们的模拟没有发现其他电子填充的 CDW 顺序特征或温度T  ≥  t /20 的顺序动量。