Abstract
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.
Highlights
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
For the superconductivity to be driven by the phonon-mechanism, the e-p coupling needs to be adequately large compared to the electron–electron (e-e) repulsive Coulomb correlation strength
With the increase in e-p coupling, both the effective onsite e-e interaction energy (Ueff ) and the effective hopping energy decrease and withUeff approaching zero, the system becomes so sensitive to the interplay between the relative strengths of these two energy scales that instead of going from a SDW phase to a CDW phase, the system prefers to settle in an intermediate phase which has been shown by Takada and Chatterjee (TC) to be metallic
Summary
A one dimensional HH system with Gaussian phonon anharmonicity may be described by the Hamiltonian. For strong e-p interaction, η → 1 , and Eq (5) generates the usual LFT36 and gives a reasonable approximation for the antiadiabatic region in which the ion motion is much faster than the electron motion. The Hamiltonian H is still not exactly soluble but it is quite reasonable to assume that after performing the four canonical transformations with generators (5), (6), (8) and (9), the electrons and phonons are weakly entangled in the Hamiltonian H and the eigenstate of H can be approximately written as the product of an electronic state |ψel (hitherto unknown) and a phonon state | ph which has to be judiciously chosen.
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