Ground-state phase diagram of the one-dimensional extended Hubbard model: A density-matrix renormalization-group approach

We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific $U,$ the critical value of Vc for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As U increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at Uc=4--6, not Uc=3 as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length $N=4M$ than for chains of $N=4M+2,$ where M is an integer, for the same U and $V.$ The difference will diminish in the thermodynamic limit.