Efficient matrix product state methods for extracting spectral information on rings and cylinders

Based on the matrix product state (MPS) formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method computing, e.g., spectral gap of quantum spin chains. This can be straightforwardly implemented top existing density-matrix renormalization group or MPS ground-state code. Although this approach is built open-boundary MPSs, also apply it to periodic conditions. Despite explicit breaking translation symmetry by representation, show that momentum emerges as good number and exploited labeling excitations ground states. We our critical Ising chain ring classical Potts model cylinder. Finally, same idea compute excitation spectra 2D infinite cylinders. Again, despite direction, recover excitations. transverse-field half-filled Hubbard model; latter, obtain accurate results for, hole dispersion cylinder circumferences up eight sites.