Matter from entangled qubits: progress and perspectives in tensor networks
Jun.-Prof. Dr. Román Orús (Johannes Gutenberg-Universität Mainz)

Tensor network states have established themselves as the natural language based on entanglement to describe and simulate quantum many-body systems. In this talk I will first provide an introduction to what tensor network states are, as well as to some of their related numerical methods. An overall perspective on the field will also be provided. Then, I will review recent progress in the field conducted in our group. This will concern the characterization of topologically-ordered 2d systems, 1d phases of matter protected by symmetries, algorithmic improvements for infinite-size 2d quantum lattice systems, spin-S Kagome Heisenberg antiferromagnets on a field, entanglement-inspired continuous unitary transformation methods, the simulation of lattice gauge theories, and the tensor network description of Kitaev’s honeycomb model. Finally, I will discuss future research directions in our group concerning the role of tensor networks in AdS/CFT, chiral topological order, and other recent ideas.