  By utilizing time-dependent tensor-network algorithms in the infinite
matrix-product-state representation, we theoretically investigate the
pump-probe spectroscopy of the one-dimensional extended Hubbard model at half
filling. Our focus lies on nonequilibrium optical conductivity and
single-particle excitation spectra. In the spin-density-wave (SDW) phase, we
identify an in-gap state in the nonequilibrium optical conductivity due to the
formation of excitons (or doublon-holon pairs), generated by the pulse through
nonlocal interactions. In the strong-coupling regime, we discern additional
multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase,
we detect not only an in-gap state but also a finite Drude weight, which
results from the dissolution of charge order by photoexcitation. Analyzing
time-dependent single-particle excitation spectra directly in the thermodynamic
limit confirms the origin of these new states in the SDW and CDW phases as the
excitation of newly emerged dispersions. We illustrate that the pump-probe
spectroscopy simulations in the thermodynamic limit furnish unambiguous
spectral structures that allow for direct comparison with experimental results,
and the integration of nonequilibrium optical conductivity and time- and
angle-resolved photoemission spectroscopy provides comprehensive insights into
nonequilibrium states.
