Many-body Entanglement and Tensor Networks

Abstract

Quantum many-body systems are difficult to study because the space of possible many-body states is huge: its dimension grows exponentially in the system size. However, in recent years progress in our understanding of quantum entanglement has revealed that only a small region of this huge state space is actually relevant to the study of quantum many-body systems.

Tensor networks are a powerful formalism developed to efficiently describe the states in this small, physically relevant region of the many-body state space. In this Colloquium I will (i) review our current understanding of many-body entanglement, (ii) introduce tensor networks as an efficient description of many-body states, and (iii) give an overview of the exciting developments within the tensor network program.