First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999