In this hands-on course, we will discuss how to adapt the traditional DMRG framework for finite-temperature applications. Using a direct approach we will focus on:

1. Truncating the Thermal Density Matrix: Extending DMRG to approximate the thermal equilibrium state by targeting the low-lying eigenstates of the Hamiltonian.
2. Partition Function Calculations: Constructing a basis that captures the dominant contributions to thermal properties at small TT.
3. Thermodynamic Quantities: Computing quantities such as energy, entropy, and correlation functions directly within the DMRG framework.
4. Small-TT Expansion: Leveraging the natural strengths of DMRG to capture low-energy excitations that dominate the physics at small temperatures.

The course emphasizes practical implementation and highlights the challenges and strategies for finite-temperature extensions in DMRG. By the end, participants will be able to apply these techniques to study thermal properties in low-dimensional quantum systems.

References will be given during the lectures.