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.