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Electron-Electron interactions, topological phase and optical properties of a charged artificial benzene ring

We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of tunneling matrix element t, Hubbard on-site repulsion U and inter-dot interaction V. In the strongly interacting case we present exact analytical results for the spectrum of the hole in a half-filled ABR dressed by spin excitations of remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin polarized (S=5/2) and maximally spin depolarised (S=1/2) states are the lowest energy, orbitally non degenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin non-degenerate but orbitally degenerate S=1/2. We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings and presence of artificial gauge can be detected optically.