Transition from half-filled stripe to Néel antiferromagnetism in the $t^{\prime }$-Hubbard model on the honeycomb lattice

We study the ground state of the doped Hubbard model on honeycomb lattice with both nearest $\left(t\right)$ and next-nearest-neighbor hoppings $\left(t^{\prime }\right)$ in the small doping and strongly interacting region. Previous study on the model without $t^{\prime }$ showed the ground state is a half-filled stripe. We employ density matrix renormalization group and extrapolate the results with truncation errors in the converged region. In the $t^{\prime }<0$ side, we find the half-filled stripe phase at $t^{\prime }=0$ is stable against the frustration of $t^{\prime }$ until a critical point $-0.4<t_c^{\prime }<-0.3$, beyond which the ground state switches to antiferromagnetic Néel phase with charge modulation. With further increase of $t^{\prime }$ to $-0.7$, the ground state becomes paramagnetic. In the $t^{\prime }>0$ side, the half-filled stripe stretches to $t^{\prime }\approx 0.7$. We do not find obvious enhancement of pairing for the range of $t^{\prime }$ studied. We study width-4 cylinders in this paper but the results for spin, charge, and pairing correlation agree qualitatively for periodic and antiperiodic boundary conditions in the half-filled stripe and antiferromagnetic Néel phases, suggesting the results are likely to be representative for true two-dimensional systems. The half-filled stripe to antiferromagnetic Néel phase transition can be realized on real materials or ultracold atom platform.