The Hubbard–Holstein Model with Anharmonic Phonons in One Dimension

抄録

Effects of cubic and quartic anharmonic phonons on the polaronic properties are investigated in the one-dimensional Hubbard–Holstein model at half filling, using the variable-displacement Lang–Firsov canonical transformation and the exact solution of Lieb and Wu. Although the quartic anharmonicity always reduces the effect of the Coulomb repulsion U, the cubic one mainly responsible for the thermal expansion of lattice brings about the effect of strong asymmetric nature in the sign of the electron–phonon coupling constant g; it enhances the effect of U for positive g, while it suppresses for negative g. As a result, the overall features of the anharmonic system are basically similar to those in the harmonic one for positive g, but even in the range of the realistic magnitudes for those anharmonicities, they may become qualitatively so different for negative g as to provide a first-order phase transition.