Agenda

Résumé : Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. These lectures will emphasize that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods (such as quantum embedding, tensor networks and various forms of quantum Monte Carlo). These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase evolves into an ordered phase at low temperature. The next nearest neighbor hopping t’ plays a key role, with low t’/t favoring stripe order and larger t’/t favoring d-wave superconductivity