Using Single-Particle Content to Distinguish Single-Particle, Collective and Strongly Correlated Atomic-Scale Quantum Systems

Linear atomic chains, such as atom chains on surfaces, linear arrays of dopant atoms in semiconductors, or linear molecules, provide ideal testbeds for studying single-particle, collective (plasmonic) and strongly correlated excitations in the quantum limit for interacting matter systems. We use exact diagonalization to find the many-body excitations of finite (4-26) atom chains, described by hopping plus long-range electron-electron repulsion and the corresponding electron-core attraction. A combination of criteria involving the many-body state transition dipole moment, balance, dynamical response, induced transition charge density and single-particle content can be used to characterize the excitations of atomic-scale systems as a function of the electron-electron interaction strength. The single-particle content clearly displays distinct transitions from a regime for single-particle excitations to collective then to strongly correlated behavior as the electron-electron interaction increases and shows how this transition takes place. This allows us to define and investigate regimes that support quantum plasmon excitations. The onset of quantum plasmons in small atomic-scale systems and the relation to Luttinger liquid theory is discussed.