Abstract
This thesis describes several topics related to finite temperature studies of strongly correlated systems: finite temperature density matrix embedding theory (FT-DMET), finite temperature metal-insulator transition, and quantum algorithms including quantum imaginary time evolution (QITE), quantum Lanczos (QLanczos), and quantum minimally entangled typical thermal states (QMETTS) algorithms. While the absolute zero temperature is not reachable, studies of physical and chemical problems at finite temperatures, especially at low temperature, is essential for understanding the quantum behaviors of materials in realistic conditions. Here we define low temperature as the temperature regime where the quantum effect is not largely dissipated due to thermal fluctuation. Treatment of systems at low temperatures is especially difficult compared to both high temperatures - where classical approximation can be applied - and zero temperatures where only the ground state is required to describe the system of interest.