We develop variational matrix product state (MPS) methods with symmetries to
determine dispersion relations of one dimensional quantum lattices as a
function of momentum and preset quantum number. We test our methods on the XXZ
spin chain, the Hubbard model and a non-integrable extended Hubbard model, and
determine the excitation spectra with a precision similar to the one of the
ground state. The formulation in terms of quantum numbers makes the topological
nature of spinons and holons very explicit. In addition, the method also
enables an easy and efficient direct calculation of the necessary magnetic
field or chemical potential required for a certain ground state magnetization
or particle density.Comment: 13 pages, 4 pages appendix, 8 figure
