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We use the composite operator method (COM) to analyze the strongly correlatedrepulsive Hubbard model, investigating the effect of nearest-neighbor hoppingsup to fourth order on a square lattice. We consider two sets of self-consistentequations, one enforcing the Pauli principle and the other imposingcharge-charge, spin-spin, and pair-pair correlations using a decoupling schemedeveloped by L. Roth. We extract three distinct solutions from these equations:COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. Anoverview of the method studying the validity of particle-hole symmetry and theLuttinger theorem for each solution is presented. Additionally, we extend theinitial basis to study superconductivity, concluding that it is induced by theVan Hove singularity. Finally, we include higher-order hoppings using realisticestimates for tight binding parameters and compare our results with ARPESmeasurements on cuprates.

Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method