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The European Physical Journal B

Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

I. V. Sankar, Ashok Chatterjee

Published Jul 1, 2014• 11 citations
Publisher
DOI
10.1140/epjb/e2014-50146-9

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This chapter introduces the Hubbard model and the Holstein-Hubbard model and discusses the charge-density wave-spin density wave transition. The most suitable model to study the interplay between the electron-phonon interaction and the Coulomb repulsion in narrow-band systems is the Holstein-Hubbard model. Krishna, Mukhopadhyay, and Chatterjee have considered an extended Holstein-Hubbard model in one dimension so that the exact Bethe ansatz solution can be taken advantage of for the effective electronic problem and employed a better phonon variational state. The chapter also discusses the nature of the self-trapping (ST) transition, particularly whether the transition is continuous or discontinuous. In view of the potential role of small polarons in high Tc superconductors and colossal magneto-resistance materials, it is certainly more important to understand the nature of the ST transition in small polaron models. Das and Sil have studied the ST transition for a many-polaron system in the two-dimensional HH model.

CRC Press eBooks•Oct 9, 2018•0 citations
The two-dimensional extended Holstein-Hubbard model (EHH) has been considered at strong correlation regime in the non-half-filled band case to understand the self-trapping transition of electrons in strongly correlated electron system. We have used the method of optimized canonical transformations to transform an EHH model into an effective extended Hubbard (EEH) model. In the strong on-site correlation limit an EH model can be transformed into a t-J model which is finally solved using Hartree-Fock approximation (HFA). We found that, for non-half-filled band case, the transition is abrupt in the adiabatic region whereas it is continuous in the anti-adiabatic region.
This chapter introduces the Hubbard model and the Holstein-Hubbard model and discusses the charge-density wave-spin density wave transition. The most suitable model to study the interplay between the electron-phonon interaction and the Coulomb repulsion in narrow-band systems is the Holstein-Hubbard model. Krishna, Mukhopadhyay, and Chatterjee have considered an extended Holstein-Hubbard model in one dimension so that the exact Bethe ansatz solution can be taken advantage of for the effective electronic problem and employed a better phonon variational state. The chapter also discusses the nature of the self-trapping (ST) transition, particularly whether the transition is continuous or discontinuous. In view of the potential role of small polarons in high Tc superconductors and colossal magneto-resistance materials, it is certainly more important to understand the nature of the ST transition in small polaron models. Das and Sil have studied the ST transition for a many-polaron system in the two-dimensional HH model.