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We develop variational matrix product state (MPS) methods with symmetries todetermine dispersion relations of one dimensional quantum lattices as afunction of momentum and preset quantum number. We test our methods on the XXZspin chain, the Hubbard model and a non-integrable extended Hubbard model, anddetermine the excitation spectra with a precision similar to the one of theground state. The formulation in terms of quantum numbers makes the topologicalnature of spinons and holons very explicit. In addition, the method alsoenables an easy and efficient direct calculation of the necessary magneticfield or chemical potential required for a certain ground state magnetizationor particle density.

Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries