New Comparisons for Local Quantities of the Two-dimensional Hubbard Model Adolfo Avella and Ferdinando Mancini

The relevance of the Hubbard model as minimal model for describing the highTc cuprate superconductors 4 and, generally, many strongly correlated materials is very well established. The model is thought to have a very rich phenomenology: a variety of spin and charge orderings (ferroand antiferromagnetic included), Mott transitions (of the Slater, Heisenberg and Hubbard types) driven by both filling and coupling , non-Fermi liquid dynamics, superconductivity caused by: magnons, static and dynamic charge ordering, proximity to quantum critical points of different origin. In particular, strong antiferromagnetic correlations are present at half-filling (and for low doping) and low temperatures. According to this, it is very relevant to have reliable solutions of this model for the variety of boundary conditions under which it can be studied. Actually, we know the exact solution only in one dimension thanks to the Bethe Ansatz. Some other few exact results are known in quite special limits, but the more relevant questions are still unsolved as the exact solution in two dimensions (which seems to be the case for the majority of the emergent highly interacting materials) is still missing. Owing to this, a huge number of approximation schemes have been proposed since the very beginning (Hubbard presented the model together with an approximate solution known today as Hubbard I) and their reliability is still under test as many physical interpretations are based on the results obtained by them. In the last decades we have seen the birth and development of many numerical methods (exact diagonalization, Lanczos, quantum Monte Carlo, ...) for studying finite clusters of bigger and bigger size. The results of these numerical methods are extremely important for the development of analytical schemes as they provide the possibility to execute unbiased tests. The numerical data can be interpreted as the experimental results relative to a specific model and any comparison with an analytical approximation scheme can be directly contrasted with its reliability. On the contrary, comparisons with real experimental data suffer of an high degree of uncertainty regarding the capability of the chosen model to capture the essential physical of the material under analysis. In this last decade, we have been developing an approximation scheme, namely the composite operator method , which proved to be quite powerful to de-