Spectral function of the spiral spin state in the trestle and ladder Hubbard model

Eder and Ohta have found a violation of the Luttinger rule in the spectral function for the ${t-t}^{\prime }-J$ model, which was interpreted as a possible breakdown of the Tomonaga-Luttinger (TL) description in models where electrons can pass each other. Here we have computed the spin correlation along with the spectral function for the one-dimensional ${t-t}^{\prime }$ Hubbard model and two-leg Hubbard ladder. By varying the Hubbard $U$ we have identified that such a phenomenon is in fact a spinless-fermion-like behavior of holes moving in a spiral spin configuration that has a spin correlation wavelength equal to the system size.