Fig. 3: Single-particle spectra for different models.
From: Traces of electron-phonon coupling in one-dimensional cuprates
a The Hubbard model (HM), c the extended Hubbard model (HM + V), and e the Hubbard-extended Holstein model (HM + g0 + g1), with increasing doping from columns 1–6. Panels b, d, f show representative momentum distribution curves (MDCs), corresponding to the cuts given by the red dashed line for each of the spectra in (a, c, e), respectively. The MDCs are chosen ~th above the bottom of the holon branch to ensure that the main holon peaks are at roughly the same position for different dopings and for different models, providing equivalent MDCs for comparison. The green and blue arrows mark the positions of the 3kF and hf branches, respectively. One can clearly see that at lower doping (<20%), adding nearest neighbor attraction V or extended e–ph coupling can enhance the hf branch while suppressing the 3kF branch. Above 20% doping, both peaks fade away quickly. Here, the energy and momentum broadening of the spectra are σω = 0.18th and σk = 2π/L. The lesser Green’s functions data corresponding to all the single-particle spectral functions displayed here can be found in Fig. S5 in Supplementary Information.
