Intertwined States at Finite Temperatures in the Hubbard Model

Significant advances in numerical techniques have enabled recent breakthroughs in the study of various properties of the Hubbard model - a seemingly simple, yet complex model of correlated electrons that has been a focus of study for more than half a century. In particular, it captures the essence of strong correlations, and is believed to possess various emergent, low energy states and collective excitations characteristic of cuprate high-temperature superconducting materials. While a thorough review of all activity is not possible here, we have focused the discussion on our recent work using unbiased, numerically exact, "brute force", finite temperature quantum Monte Carlo methods. Our various studies reveal a rich variety of quantum liquid crystal phases, and complementary transport properties, which answer some questions, but certainly raise others concerning "strange metal" behavior and the ultimate fate of quasiparticles in the Hubbard model.