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AIP conference proceedings

The Holstein-Hubbard model with Gaussian anharmonicity in one-dimension at half filling

Ch. Uma Lavanya, Ashok Chatterjee

Published Jan 1, 2016• 1 citation
Publisher

Abstract

The Holstein-Hubbard model(HHM) with Gaussian anharmonicityis studied at half filling in one-dimension using a variational method based on a series of canonical transformations. It is shown that the anharmonicityincreases the width of the intermediate metallic phase at the SDW-CDW crossover region.
DOI
10.1063/1.4946528

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AIP conference proceedings•Jan 1, 2019•0 citations
The Holstein-Hubbard model with Gaussian phonon anharmonicity is studied in one-dimension at half filling using a variational method based on a series of canonical transformations. A fairly accurate phonon state is chosen to average the transformed Holstein-Hubbard Hamiltonian to obtain an effective Hubbard model which is then solved using the exact Bethe - ansatz following Lieb and Wu to obtain the ground state energy, the average lattice displacement and the renormalized parameters. The Mott-Hubbard criterion, local spin moment and the von Neumann entropy (which is a measure of quantum entanglement) are calculated to determine the ground state phase diagram which shows that the width of the metallic phase flanked by the SDW and CDW phases increases with increasing anharmonicity at low and moderate values of anharmonicity but eventually saturates when the anharmonicity becomes substantially large.
Abstract The one-dimensional Holstein–Hubbard model is analyzed at half filling at the CDW-SDW transition region by using a series of unitary transformations. The phonon degrees of freedom are eliminated by averaging the transformed Hamiltonian with respect to a generalized many-phonon state and the resulting effective electronic Hamiltonian is finally solved exactly by employing the Bethe-ansatz technique. The present variational state leads to a lower ground state energy as compared to those obtained from the previous variational calculations and yields a wider intermediate metallic phase at the SDW-CDW transition region confirming the prediction of Takada and Chatterjee.
The Holstein–Hubbard model is considered to study the competition between the electron-phonon interaction and the electron-electron interaction in a one-dimensional correlated Fermi system at half-filling. First, a series of canonical transformations that incorporate phonon coherence and correlation effects is performed and then the transformed Hamiltonian is averaged with respect to a zero-phonon state. The resulting effective electronic Hamiltonian is finally solved exactly by the Bethe-ansatz technique. It is shown that the present method suggests the existence of a wider intermediate metallic phase at the SDW-CDW crossover region than the one predicted by the simple variational method of Takada and Chatterjee. The presence of this metallic phase is indeed a favorable situation from the point of view of high temperature superconductivity.
The half-filled one-dimensional Holstein-Hubbard model presents, at zero temperature, a charge-density-wave (CDW) phase and a Mott insulator phase. Recent results have shown that the transition from one phase to the other might proceed through an intermediate metallic phase. In this work, we determine the CDW phase boundary using the variational cluster approximation. Using exact diagonalization and cluster perturbation theory, we study both the pair susceptibility and the spectral gaps in the non-CDW part of the phase diagram. We cannot rule out the existence of an intermediate metallic phase.
The Holstein–Hubbard model is considered to study the competition between the electron-phonon interaction and the electron-electron interaction in a one-dimensional correlated Fermi systemat half-filling. First, a series of canonical transformations that incorporate phonon coherence and correlation effectsis performed and then the transformed Hamiltonian is averaged with respect to a zero-phonon state. The resulting effective electronic Hamiltonian is finally solved exactly by the Bethe-ansatz technique. It is shown that the present method suggests the existence of a wider intermediate metallic phase at the SDW-CDW crossover region than the one predicted by the simple variational method of Takada and Chatterjee. The presence of this metallic phase is indeed a favorable situation from the point of view of high temperature superconductivity.