Quantum phase transitions of the one-dimensional Peierls-Hubbard model with next-nearest-neighbor hopping integrals

Abstract

We investigate two kinds of quantum phase transitions observed in the one-dimensional half-filled Peierls-Hubbard model with the next-nearest-neighbor hopping integral in the strong-coupling region $U\ensuremath{\gg}t$, ${t}^{\ensuremath{'}}$ [$t$ ${(t}^{\ensuremath{'}})$, nearest- (next-nearest-) neighbor hopping; $U$, on-site Coulomb repulsion]. In the uniform case, with the help of the conformal field theory prediction, we numerically determine a phase boundary ${t}_{\mathrm{c}}^{\ensuremath{'}}(U/t)$ between the spin-fluid and the dimer states, where a bare coupling of the marginal operator vanishes and the low-energy and long-distance behaviors of the spin part are described by a free-boson model. To exhibit the conformal invariance of the systems on the phase boundary, a multiplet structure of the excitation spectrum of finite-size systems and a value of the central charge are also examined. The critical phenomenological aspect of the spin-Peierls transitions accompanied by the lattice dimerization is then argued for the systems on the phase boundary; the existence of logarithmic corrections to the power-law behaviors of the energy gain and the spin gap (i.e., the Cross-Fisher scaling law) are discussed.