Phase transitions in the one-dimensional modified Penson-Kolb model with density-dependent hopping

By relaxing the conventional assumption of the equal one-electron hopping amplitude, we modify the one-dimensional half-filled Penson-Kolb (PK) model to obey the density-dependent hopping (DDH). For positive small modulation parameter [Formula: see text] and pair hopping [Formula: see text], we use bosonization and renormalization-group analysis to determine the ground state phase diagram. In the attractive case([Formula: see text]), the existence of the DDH leads to a gap transition in the spin sector and produces a fully gapless phase where a Luttinger liquid metal phase with dominant triplet superconducting correlations is realized for [Formula: see text], with the charge transition point [Formula: see text] and the spin transition point [Formula: see text]. Besides, there is a Luther-Emery matal phase with dominant singlet-superconducting correlations for [Formula: see text] and a Haldane insulator phase characterized by dominant bond-spin-density-wave correlations for [Formula: see text] in the repulsive regime ([Formula: see text]).