Symmetry-enhanced spectral analysis via the spectral method and filter diagonalization

A symmetry-adapted propagation scheme is introduced to enhance the efficiency of spectral analysis using either the spectral method or filter diagonalization. The essence of the method is to project out symmetry components from a single wave packet that contains all the symmetry species. These components are then used to recover the spectrum and/or energy wave functions for each symmetry species. The adaptation of symmetry not only facilitates the symmetry assignment of the eigenstates, but also reduces the number of propagation steps because the density of states for individual symmetry species is typically much lower than that of the overall spectrum. Our approach is numerically superior to the conventional symmetry-adapted methods because the propagation of multiple wave packers is avoided. A simplified atomic model with two one-dimensional electrons is used as a numerical example.