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We study a 1D lattice Hamiltonian, relevant for a wide range of interestingphysical systems like, e.g., the quantum-Hall system, cold atoms or moleculesin optical lattices, and TCNQ salts. Through a tuning of the interactionparameters and a departure from a strictly convex interaction, nontrivialground-state degeneracies and fractionally charged excitations emerge. Theexcitations, being a generalization of the fractional charges known from thefractional quantum-Hall effect, appear as domain walls between inequivalentground states and carry the charge +e/mq or -e/mq, where m is an integer andassociated with the specified interaction, and v = p/q is the filling fractionin the lattice. The description points at an interesting resemblance to statesconnected to non-Abelian statistics, which is central for the concept oftopological quantum computing.

Nontrivial ground-state degeneracies and generalized fractional excitations in the 1D lattice