Electrons Hopping across a Molecular Network: Spectra and Symmetries

We investigate interacting spinless electrons on finite molecular ring networks described by a tight-binding Hubbard Hamiltonian. The interplay between lattice geometry, Coulomb interactions and discrete symmetries is analysed for rings with $L=3,4,5,6$ nodes, filled with one, two or three electrons. Special attention is devoted to the role of the network symmetries in determining the structure of the many-body spectrum and the Mulliken classification of the eigenstates. Using group-theoretical methods, we examine the evolution of the spectra in the presence of an external magnetic flux. The Zeeman effect lifts degeneracies and results in combination with the Coulomb interaction to avoided crossings in symmetry sectors. We identify a qualitatively distinction between systems with an even and odd number of particles. At half-filling, particle-hole symmetry (duality) protects selected symmetry sectors against Zeeman splitting.