This course will be given by Prof. Dr. Karen Hallberg during October-December 2021.
Abstract:
In this course I will focus on how to deal numerically with quantum many-body problems and materials with strongly interacting electrons. After a brief review on why these systems can be considered among the most challenging and interesting problems in physics, I will present some of the state-of-the-art numerical techniques used to calculate ground state and dynamical properties of paradigmatic models of these materials. These methods include the Density Matrix Renormalization Group (DMRG), Matrix Product States and, in general, Tensor Network techniques. The success of these methods relies on a very efficient optimization of the quantum states involved, which appeals to basic concepts of quantum information, which I will explain in detail.
This course includes practical written and hands-on exercises and the reading of some of the most
recent reviews and papers on these topics.
Outline:
1. Why are strongly correlated materials interesting?
A brief review on their physical properties
2. Why are strongly correlated materials difficult to study theoretically?
Computational complexity
3. Brief review of current numerical methods for strongly correlated systems
4. Density matrix renormalization: how to optimize the information
- Real space renormalization.
- DMRG
- Quantum Information and entanglement in many-body systems
- Dynamics
5. Other Tensor Networks
- Matrix Product States and Operators
- Multiscale entanglement (MERA, PEPS)
- Time evolution
