Tensor network states are used to describe physical states and processes in many-body physics and related disciplines. An explicit connection between these current methods and the diagrammatic methods known in category was made in the following paper.
Jacob Biamonte later taught a course explaining these results and exploring tensor networks in more detail.
Here are some review articles on tensor network states:
F. Verstraete, J.I. Cirac and V. Murg, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Adv. Phys. 57 (2008), 143.
J. I. Cirac and F. Verstraete, Renormalization and tensor product states in spin chains and lattices, J. Phys. A 42 (2009), 504004.
Guifre Vidal, Entanglement renormalization: an introduction.
Vidal has written extensively about tensor networks, including:
Fermionic MERA:
Fermionic PEPS:
Fermionic quantum circuits:
Vidal pointed out in
that tensor network states made of symmetric tensors were nothing but spin networks as used in loop quantum gravity. He suggests that this could lead to new interactions between different subjects. See also.
Last revised on May 29, 2012 at 22:04:00. See the history of this page for a list of all contributions to it.