发表机构
Texas A&M University; University of Minnesota（德克萨斯农工大学; 明尼苏达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明自能极点不一定违反Luttinger定理：在两类含带隙能带与窄准粒子带的模型中，模型I对任意正残余权重均保持Luttinger-Ward分析有效，模型II在残余权重超过临界值后恢复有效性。
AI 中文摘要
Luttinger定理将费米面体积与每个自旋的电子密度$n$联系起来。该定理在任意费米液体中成立，但人们普遍认为当费米子自能具有极点时，该定理会被破坏。我们表明情况并非必然如此。作为示例，我们考虑一个由两个带隙能带组成的费米子系统，该系统源于具有极点的自能$\Sigma (\omega, \mathbf{k})$，以及一个跨越$\omega =0$的窄残余准粒子能带，其残余权重$Z \ll 1$（残余费米液体）。我们考虑模型I，其中$Z$也将准粒子带宽$W$重整化为$ZW$；以及模型II，其中$W$保持未重整化。此类系统的格林函数$G(\omega, \mathbf{k})$包含两个零点和三个极点——一个来自准粒子能带，两个来自带隙能带。然而，我们表明，在模型I中，Luttinger-Ward分析对于任何$Z >0$都完全适用，结果与带隙能带不存在时完全相同。对于模型II，一旦$Z$超过某个临界值（该值取决于费米子密度），Luttinger-Ward分析即恢复适用。
英文摘要
Luttinger theorem relates Fermi surface volume to electron density per spin $n$. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, originating from a self-energy $Σ(ω, \mathbf{k})$ with a pole, and a narrow residual quasiparticle band crossing $ω=0$, with a small residue $Z \ll 1$ (a residual Fermi liquid). We consider Model I, in which $Z$ also renormalizes quasiparticle bandwidth $W$ to $ZW$ and Model II, in which $W$ remains unrenormalized. The Green's function for such a system $G(ω, \mathbf{k})$ contains two zeros and three poles --- one from the quasiparticle band and two from the gapped bands. Yet, we show that in Model I, the Luttinger-Ward analysis is fully applicable for any $Z >0$, and the results are exactly the same as if the gapped bands did not exist. For Model II, the Luttinger-Ward analysis recovers once $Z$ exceeds some critical value, which depends on fermionic density.
Comments9 pages, 7 figures
