Phase diagram of the half-filled Hubbard chain with next-nearest-neighbor hopping

We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the Density-Matrix Renormalization Group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion $U$, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak $U$, sufficiently large next-nearest-neighbor hopping $t_2$ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As $U$ is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.