  We study the one dimensional t-t'-J model for generic couplings using two
complementary theories, the extremely correlated Fermi liquid theory and
time-dependent density matrix renormalization group over a broad energy scale.
The two methods provide a unique insight into the strong momentum dependence of
the self-energy of this prototypical non-Fermi liquid, described at low
energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate
relationship to spin-charge separation, i.e. the splitting of Landau
quasiparticles of higher dimensions into two constituents, driven by strong
quantum fluctuations inherent in one dimension. The momentum distribution
function, the spectral function, and the excitation dispersion of these two
methods also compare well.
