Momentum distribution and tunneling density of states of one-dimensional Fermionic [Formula: see text] Hubbard model

We study the one-dimensional Fermionic Hubbard model with [Formula: see text] spin symmetry in the incommensurate filling case. The basic properties of Green's function, momentum distribution and tunneling density of states of the system at low temperature are studied in the frame work of Luttinger liquid theory combined with Bethe Ansatz solutions for arbitrary interaction. In the strong interacting case, the system enters the spin-incoherent regime at intermediate temperature [Formula: see text] and we obtain the Green's function and tunneling density of states by generalizing the path integral approach for the [Formula: see text] case to the [Formula: see text] case in this regime. The theoretical results we obtained agree qualitatively with the experiments on the one-dimensional alkaline earth atomic system with [Formula: see text] spin symmetry. The similarities and difference between the one-dimensional [Formula: see text] Fermionic Hubbard system at large N and the one-dimensional spinless Bosonic system are also investigated.