The validity of the strong-coupling expansion of the two-dimensional Hubbard model is questioned. We present evidence of disagreement between the strong-coupling expansion and the exact solution of the Hubbard model on small lattices.

Physical review. B, Condensed matterSep 1, 19898 citations

Journal of Magnetism and Magnetic Materials

Strong coupling regime in the two-dimensional Hubbard model

Ian P. McCulloch, M. Gulácsi

Published May 1, 1998• 0 citations

Publisher

DOI: 10.1016/s0304-8853(98)00018-3

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Validity of the strong-coupling expansion of the two-dimensional Hubbard model

Barry Friedman, X. Y. Chen, W. P. Su

Physical review. B, Condensed matterSep 1, 19898 citations

In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization

{V}_{\mathbf{k}}

on the superconductivity. In the strong-coupling regime and for a

d

-wave superconducting gap, we have obtained the superconducting critical temperature

{T}_{c}

and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential

U

, the gap increases for low temperatures and diminishes as the temperatures increase toward

{T}_{c}

. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and

{T}_{c}

, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as

U

increases. The relation between applied pressure

P

and hybridization in the strong-coupling regime is also discussed.