A time and momentum resolved tunneling spectroscopy approach to non-equilibrium phenomena in correlated systems

We introduce a numerical method to calculate the spectral density of correlated systems using a tunneling approach efficiently implemented through the time-dependent Density Matrix Renormalization-Group (tDMRG). By using an extended probe, which is basically a copy of the system of interest, we are able to extract the time-resolved spectrum with the momentum information of the excitations. We illustrate our ideas by calculating the time-resolved spectrum of a Mott-insulating extended Hubbard chain after a sudden quench. Our results demonstrate that the system realizes a non-thermal state that contains an admixture of spin and charge density excitations, with corresponding signatures recognizable as in-gap subbands. In particular, we identify a band of excitons and one of stable anti-bound states at high energies that gains enhanced visibility after the pump. We do not appreciate noticeable relaxation within the time-scales considered, which is attributed to the lack of decay channels due to spin-charge separation.