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Advances in Condensed Matter Physics
Volume 2010 (2010), Article ID 350787, 14 pages
Review Article

Existence of an Intermediate Metallic Phase at the SDW-CDW Crossover Region in the One-Dimensional Holstein-Hubbard Model at Half-Filling

School of Physics, University of Hyderabad, Hyderabad 500 046, India

Received 5 September 2009; Accepted 8 December 2009

Academic Editor: Alexandre Sasha Alexandrov

Copyright © 2010 Ashok Chatterjee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.