Lecturer: Mari Carmen Banuls
Affiliation: Max-Planck Institute for Quantum Optics, Garching, Germany
Abstract: The term Tensor Network States (TNS) has become a common one in the context of numerical studies of quantum many-body problems. It refers to a number of families that represent different ansatzes for the efficient description of the state of a quantum many-body system. The first of these families, Matrix Product States (MPS), lies at the basis of Density Matrix Renormalization Group methods, which have become the most precise tool for the study of one dimensional quantum many-body systems. Their natural generalization to two or higher dimensions, the Projected Entanglement Pair States (PEPS) are good candidates to describe the physics of higher dimensional lattices. They can be used to study equilibrium properties, as ground and thermal states, but also dynamics.
Quantum information gives us some tools to understand why these families are expected to be good ansatzes for the physically relevant states, and some of the limitations connected to the simulation algorithms.
The first part of these lectures will introduce the basic concepts of TNS. The main formal properties of the one-dimensional MPS ansatz, and the more general PEPS will be reviewed, as well as the basic algorithms used to find equilibrium and non-equilibrium states.
In the second part, I will present concrete applications that somehow extend the applicability of these tools, for instance for the study of lattice gauge theories and open quantum systems.