CMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Series: Superconductivity, Stripes, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model?
Antoine Georges - Collège de France, Paris and Flatiron Institute, New York
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. In this talk, I will argue 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. 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 may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.