Optical excitations in atomic-scale materials can be strongly mixed, with contributions from both single-particle transitions and collective response. This complicates the quantum description of these excitations, because there is no clear way to define their quantization. To develop a quantum theory for these optical excitations, they must first be characterized so that single-particle-like and collective excitations can be identified. Linear atomic chains, such as atom chains on surfaces, linear arrays of dopant atoms in semiconductors, or linear molecules, provide ideal testbeds for studying collective excitations in small atomic-scale systems. We use exact diagonalization to study the many-body excitations of finite (10 to 25) linear atomic chains described by a simplified model Hamiltonian. Exact diagonalization results can be very different from the density functional theory (DFT) results usually obtained. Highly correlated, multiexcitonic states, strongly dependent on the electron—electron interaction strength, dominate the exact spectral and optical response but are not present in DFT excitation spectra. The ubiquitous presence of excitonic many-body states in the spectra makes it hard to identify plasmonic excitations. A combination of criteria involving a many-body state’s transfer dipole moment, balance, transfer charge, dynamical response, and induced-charge distribution do strongly suggest which many-body states should be considered as plasmonic. This analysis can be used to reveal the few plasmonic many-body states hidden in the dense spectrum of low-energy single-particle-like states and many higher-energy excitonic-like states. These excitonic states are the predominant excitation because of the many possible ways to develop local correlations.

中文翻译：

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接近等离子体的量子极限：线性原子链

原子级材料中的光激发可以强烈混合，单粒子跃迁和集体响应都有贡献。这使这些激发的量子描述变得复杂，因为没有明确的方法来定义它们的量化。要为这些光激发开发量子理论，必须首先对它们进行表征，以便可以识别出类单粒子和集体激发。线性原子链，例如表面上的原子链、半导体中掺杂原子的线性阵列或线性分子，为研究小原子尺度系统中的集体激发提供了理想的测试平台。我们使用精确对角化来研究由简化模型哈密顿量描述的有限（10 到 25）线性原子链的多体激发。精确的对角化结果可能与通常获得的密度泛函理论 (DFT) 结果大不相同。高度相关的多激子态，强烈依赖于电子-电子相互作用强度，支配着精确的光谱和光学响应，但不存在于 DFT 激发光谱中。光谱中普遍存在的激子多体状态使得很难识别等离子体激发。涉及多体状态的转移偶极矩、平衡、转移电荷、动力学响应和感应电荷分布的标准组合确实强烈建议哪些多体状态应被视为等离子体。这种分析可用于揭示隐藏在低能类单粒子态和许多高能激子态的密集光谱中的少数等离子体多体态。这些激子态是主要的激发，因为有许多可能的方式来发展局部相关性。