Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Abstract

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X. They generate relevant terms proportional to X 2 in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U = U c and a spin transition at U = U s > U c . For U < U c singlet superconducting correlations dominate, while for U > U s , the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values U c < U < U s , the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X = 0 . We obtain that the charge transition remains at U c = 0 for X ≠ 0 . Solving the RG equations for the spin sector, we provide an analytical expression for U s ( X ) . The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X < t / 2 where t is the hopping.