Exact Solution of The Anharmonic Electron-Phonon Problem

Marco Zoli

J. Fricke, V. Meden, C. Wöhler +1 more

Ashok Chatterjee, Yasutami Takada

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.

Wilfried Schäfer, Martin Wegener

Debika Debnath, Mohammed Zahid Malik, Ashok Chatterjee

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott-Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron-phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Eric Jeckelmann, Chunli Zhang, Steven R. White