Recent progress in computational studies of the two-dimensional Hubbard model

I will discuss some of the recent developments in many-body computational studies to understand properties of the two-dimensional Hubbard model. As a fundamental model in quantum many-body physics, the Hubbard model has presented a tremendous challenge, with multiple competing tendencies and its properties often the outcome of a delicate balance of their competition and coexistence. This places extermely demanding requirements on numerical approaches, including high precision, excellent predictive power and accuracy, and reliable access to the thermynamic limit. Progress in method development and the combined use of complementary methods have led to significant recent progress. I will introduce some of the methological advances in both ground-state and finite-temperature auxiliary-field quantum Monte Carlo (AFQMC), and discuss joint efforts using AFQMC and other state-of-the-art methods to determine the nature of magnetic and pairing orders in the two-dimensional Hubbard model.