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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 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.

I am most grateful for collaborations on this topic with Michel Ferrero, Yuan-Yao He, Marcel Klett, Evgeny Kozik, Olivier Parcollet, Riccardo Rossi, Mathias Scheurer, Fedor Simkovič, Subir Sachdev, Miles Stoudenmire, André-Marie Tremblay, Alexander Wietek, Nils Wentzell, Steve White, Wei Wu, Bo Xiao and Shiwei Zhang.

Please register at the doodle so that we know how much pizza to get!

Location: Science 1, Room 102
Time: Friday 31 March 2023, 12:00 for pizza, 12:30 start discussion