Phase diagram of the t-U-J1-J2 chain at half filling
  We investigate the half-filled Hubbard chain with additional nearest- and next-nearest-neighbor spin exchange, J1 and J2, using bosonization and the density-matrix renormalization group. For J2 = 0 we find a spin-density-wave phase for all positive values of the Hubbard interaction U and the Heisenberg exchange J1. A frustrating spin exchange J2 induces a bond-order-wave phase. For some values of J1, J2 and U, we observe a spin-gapped metallic Luther-Emery phase. 
X. Huang, E. Szirmai, F. Gebhard, J. S\'olyom, and R.M. Noack