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physica status solidi (b)

The properties of the CDW phase in the weak coupling anharmonic Holstein–Hubbard model

Przemysław R. Grzybowski

Published Jan 1, 2006• 2 citations
Publisher

Abstract

Abstract The anharmonic Holstein–Hubbard Hamiltonian in the case of weak effective electron–electron attraction is studied. To deal with anharmonicity of phonons, variational canonical transformations are used to derive an effective electron Hamiltonian. The properties of the charge density wave (CDW) phase, for half‐filling, are analyzed using this effective Hamiltonian. In particular, the critical temperatures, gap function, order parameter and gap ratio are calculated. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200562501

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Abstract The anharmonic Holstein–Hubbard Hamiltonian in the case of weak effective electron–electron attraction is studied. To deal with anharmonicity of phonons, variational canonical transformations are used to derive an effective electron Hamiltonian. The properties of the charge density wave (CDW) phase, for half‐filling, are analyzed using this effective Hamiltonian. In particular, the critical temperatures, gap function, order parameter and gap ratio are calculated. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of this anharmonic term reduces the extent of the charge density wave (CDW) phase at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first-order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the superconducting susceptibility in the doped region and show that anharmonicity can enhance the superconducting response.
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 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.