Superconductivity in the two-dimensional Hubbard model

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

We use the composite operator method (COM) to analyze the strongly correlated repulsive Hubbard model, investigating the effect of nearest-neighbor hoppings up to fourth order on a square lattice. We consider two sets of self-consistent equations, one enforcing the Pauli principle and the other imposing charge-charge, spin-spin, and pair-pair correlations using a decoupling scheme developed by Roth (1969Phys. Rev.184451-9). We extract three distinct solutions from these equations: COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. An overview of the method studying the validity of particle-hole symmetry and the Luttinger theorem for each solution is presented. Additionally, we extend the initial basis to study superconductivity, concluding that it is induced by the Van Hove singularity. Finally, we include higher-order hoppings using realistic estimates for tight binding parameters and compare our results with ARPES measurements on cuprates.

Evaluation of the two-particle propagator for the Hubbard model with the help of the Hubbard-I approximation

The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for the Hubbard model on a two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada (2007 J. Phys. Soc. Japan 76 113708) in the limit of strong electron-electron interaction. The Hubbard-I predictions are in good qualitative agreement with the Monte Carlo results. In particular, d-wave correlations decay as cr( - 3) ('free-electron' behaviour) if the separation r exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates the coefficient c by a factor of about 3. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of r.