tensor network



Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products



Internal monoids



In higher category theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



The term tensor network has become popular in quantum physics for essentially what in mathematical physics is known as Penrose notation and in monoidal category theory is referred to as string diagrams.

The term rose to prominence in quantum physics partly with discussion of finite quantum mechanics in terms of dagger-compact categories but then mainly via its use in holographic entanglement entropy

For finite quantum mechanics in \dagger-compact categories

Application to finite quantum mechanics in terms of dagger-compact categories… (see there).

For holographic entanglement entropy

Application to holographic entanglement entropy (…)

graphics grabbed from Harlow 18

graphics grabbed from Harlow 18

In this context the Ryu-Takayanagi formula for holographic entanglement entropy has an exact proof PYHP 15, Theorem 2.



Relation to spin chains:

  • Mari Carmen Banuls, Michal P. Heller, Karl Jansen, Johannes Knaute, Viktor Svensson, From spin chains to real-time thermal field theory using tensor networks (arXiv:1912.08836)

In holographic entanglement entropy

The use of tensor networks as a tool in holographic entanglement entropy goes back to

  • Brian Swingle, Entanglement Renormalization and Holography (arXiv:0905.1317)

  • Brian Swingle, Constructing holographic spacetimes using entanglement renormalization (arXiv:1209.3304)

Further interpretation in terms of quantum error correcting codes is due to

reviewed in

Discussion in the context of the p-adic AdS/CFT correspondence:

See also

In higher parallel transport

Discussion in relation to higher parallel transport:

Last revised on January 8, 2020 at 08:25:36. See the history of this page for a list of all contributions to it.