We report on a strong coupling approach (on-site Coulomb repulsion, U larger than the nearest-neighbor hopping energy
∣t∣) to the Hubbard model. Starting from the Hubbard operators that diagonalize the interaction term, we generate a hierarchy of composite operators from the equations of motion. Using the Hubbard operators as a basis, we are able to compute the associated Green functions including the anomalous Green functions that describe pair formation. We show explicitly that these anomalous Green functions are nonzero in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel; however, the entities that pair up are not single-electron-like particles but rather composite excitations (that we call cexons) made out of an electron and a hole on nearest-neighbor sites. Cexons are fermionic in nature as they have spin 1/2 and also have unit charge. Our calculations of the chemical potential reveal that negative compressibility in the 2D Hubbard model and composite excitation pairing are intimately connected, namely, the larger the negative compressibility, the larger the pairing amplitude. Our observation of negative compressibility in the underdoped regime is consistent with phase segregation or stripe formation in the normal state. While pairing ameliorates the negative compresssibility, it does not eliminate it entirely. In addition, we find that the anomalous correlation functions are particle-hole symmetric and exhibit a maximum at a doping level of roughly
10 as measured from half-filling. For
U=8∣t∣, the onset temperature for pair formation is
0.02∣t∣. The effect of nearest-neighbor Coulomb repulsions is discussed.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on
La1.28Nd0.6Sr0.12CuO4.