John Baez
Tensor Network States

About

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.

Background reading

Here are some review articles on tensor network states:

Vidal has written extensively about tensor networks, including:

Fermionic Tensor Network States

Fermionic MERA:

Fermionic PEPS:

  • http://arxiv.org/abs/0904.4667, http://arxiv.org/abs/0912.0646

Fermionic quantum circuits:

  • http://arxiv.org/abs/0905.0669, http://arxiv.org/abs/0907.3689

Anyonic tensor network states

  • http://arxiv.org/abs/1006.2478, http://arxiv.org/abs/1006.3532

Connection to spin networks and category theory

Vidal pointed out in

  • http://arxiv.org/abs/0907.2994

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.