nLab Levin-Wen model

Idea

The Levin-Wen model is lattice model for certain phenomena in 2-dimensional solid state physics. It can be regarded as a 3d TQFT.

Related concepts

• The 4d TQFT analog of the Levin-Wen model is the Walker-Wang model.

• topological order

• string-net model

References

The original article:

• Michael Levin, Xiao-Gang Wen, String-net condensation: A physical mechanism for topological phases, Phys.Rev. B 71 (2005) 045110 $[$arXiv:cond-mat/0404617$]$

Discussion of the Levin-Wen model as an extended 3d TQFT formulated using tensor categories:

• Alexei Kitaev, Liang Kong, Levin-Wen models and tensor categories [pdf]

See also:

• Liang Chang, Meng Cheng, Shawn X. Cui, Yuting Hu, Wei Jin, Ramis Movassagh, Pieter Naaijkens, Zhenghan Wang, Amanda Young: On Enriching the Levin-Wen model with Symmetry, J. Phys. A: Math. Theor. 48 (2016) 12FT01 [arXiv:1412.6589]

• Vincentas Mulevicius, Ingo Runkel, Thomas Voß: Internal Levin-Wen models [arXiv:2309.05755]

• Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, David Penneys: Levin-Wen is a gauge theory: entanglement from topology [arXiv:2401.13838]

On anyonic topological order in the Levin-Wen model:

• Jessica Christian, David Green, Peter Huston, David Penneys: A lattice model for condensation in Levin-Wen systems [arXiv:2303.04711]

and using rigorous DHR superselection theory:

• Alex Bols: Sector theory for Levin-Wen models, talk at CQTS (Nov 2025) [slides:pdf]