PHY 771.02, Tensor network state methods, Fall 2017
| Instructor: | Prof. Thomas Barthel |
| Lectures: | Mondays 12:00-1:15PM in Physics 299 |
| Office hours: | Mondays and Fridays 2:40-3:45PM in Physics 287 |
Synopsis
Tensor network states are a recent and very successful (numerical) approach for the investigation of strongly-correlated quantum many-body systems that is not bothered by the sign problem of quantum Monte Carlo. It is applied mostly for studies of condensed matter, ultracold atomic gases, and quantum chemistry.We will discuss:
- The density-matrix renormalization group (DMRG) in its traditional interpretation of Hilbert space decimation. This allows for the approximation of the many-body ground state, often to machine precision.
- The DMRG in the modern formulation of matrix product states (MPS).
- Generalizations for the study of non-equilibrium phenomena and the computation of response functions as, e.g., measured in ARPES and neutron scattering experiments.
- Generalizations for the study of finite-temperature states using purifications of density operators and so-called minimally entangled typical thermal states.
- Modifications for the study of open quantum systems (decoherence etc.)
- Scaling of entanglement entropies in quantum many-body systems. This allows us to bound the computational complexity of the MPS methods.
- Generalizations to higher dimensions and connections to real-space renormalization group: projected entangled pair states (PEPS) and the multi-scale entanglement renormalization ansatz (MERA).
have a nice day!