Abstract
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.