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AIP conference proceedings

Existence of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the 1-D Hubbard-Holstein model at half filling

Mohammed Zahid Malik, Soma Mukhopadhyay, Ashok Chatterjee

Published Jan 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.5113214

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Scientific Reports•Jun 10, 2021•10 citations
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 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.
The Hubbard-Holstein model is studied at half filling in one dimension using a variational method based on the variable-displacement Lang-Firsov canonical transformation and the exact solution to the Hubbard model due to Lieb and Wu. It is usually believed that the system undergoes a direct insulator-to-insulator transition from charge-density wave (CDW) to spin-density wave (SDW) with the increase of the on-site Coulomb repulsion U for a given strength of the electron-phonon coupling. Here, we show indications that, at least in the antiadiabatic region, an intervening metallic state may exist in the crossover region of the CDW-SDW transition.
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 serves as a useful framework to investigate this interplay between the phonon-induced electron-electron attractive interaction and the direct Coulomb repulsion and can afford interesting phase diagrams due to competition among charge-density wave (CDW), spin-density wave (SDW), and superconductivity. However the detailed nature of the CDW-SDW transition is still not very well known. It is generally believed that the system undergoes a direct insulator to insulator transition from CDW to SDW with the increase of the on-site Coulomb repulsion for a given strength of the electron-phonon coupling and this is the main bottleneck for the polaronic/bipolaronic mechanism of high-temperature superconductivity. We have recently made an investigation to study the nature of the transition from SDW phase to CDW phase within the framework of a one-dimensional Holstein-Hubbard model at half-filling using a variational method. We find that an intervening metallic phase may exist at the crossover region of the CDW-SDW transition. We have also observed that if the anharmonicity of the phonons is taken into account, this metallic phase widens and the polarons become more mobile, which is a more favorable situation from the point of view of superconductivity. We shall finally show that an improved variational calculation widens the metallic phase and makes the polarons more mobile, which reconfirms the existence of the intermediate metallic phase at the SDW-CDW crossover region.
We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.
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.