An introduction to Tree Tensor Networks and Mera in the context of one and two dimensional many body quantum systems

Luca Tagliacozzo

Barcelone

Mon, Nov. 29th 2010, 14:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

In this talk I will review the ideas behind the use of Tensor Network simulations to obtain the ground state of many body quantum systems in one and two dimensions. I will then focus on two types of Tensor Network ansatz, the Tree Tensor Network and the Mera. I will explain how they both encode the state of the system through a coarse graining procedure but differ on their approach to treat entanglement. While the Tree Tensor Network can be seen as a variation of the Density Matrix Renormalization Group, the Mera implements the real space Renormalization group transformation called Entanglement Renormalization. By the end of the talk it will become clear that this difference leads to a different range of applicability of the two ansatz, while the Tree Tensor network has been mostly used to obtain precise information of finite (small) size systems, the Mera is more suited to study infinite systems and their structure of renormalization group fixed points. \\ \\ (Recommended references on the topic: \\ Tree Tensor Network arXiv:0903.5017v2 \\ Entanglement Renormalization and the MERA arXiv:0912.1651v2)

Contact : Gregoire
MISGUICH