basics
Examples
quantum algorithms:
In condensed matter theory, string-net models were introduced as lattice models for 2-dimensional topological phases of matter exhibiting topological order. The name essentially derives from the fact that the main degrees of freedom are located on the lattice edges.
Original articles:
Michael Levin, Xiao-Gang Wen, String-net condensation: A physical mechanism for topological phases, Phys.Rev. B 71 (2005) 045110 arXiv:cond-mat/0404617
(see also at Levin-Wen model)
Michael Levin, Xiao-Gang Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett., 96, 110405 (2006) (arXiv:cond-mat/0510613)
(introducing topological entanglement entropy with regards to string-net models)
In terms of tensor networks:
O. Buerschaper, M. Aguado, G. Vidal, Explicit tensor network representation for the ground states of string-net models, Phys. Rev. B 79 (2009) 085119 arXiv:0809.2393, doi:10.1103/PhysRevB.95.195110
Zheng-Cheng Gu, Michael Levin, Brian Swingle, Xiao-Gang Wen, Tensor-product representations for string-net condensed states, Phys. Rev. B 79 (2009) 085118 doi:10.1103/PhysRevB.79.085118
Further development:
Ling-Yan Hung, Yidun Wan, String-Net Models with Fusion Algebra, Phys. Rev. B 86 (2012) 235132 arXiv:1207.6169
Chien-Hung Lin, Multi-flavor string-net models, Phys. Rev. B 95 195110 (2017) arXiv:1611.08288, doi:10.1103/PhysRevB.95.195110
Review and exposition:
Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen:
Sections 6.4-6.9 in: Quantum Information Meets Quantum Matter – From Quantum Entanglement to Topological Phases of Many-Body Systems, Quantum Science and Technology (QST), Springer (2019) arXiv:1508.02595, doi:10.1007/978-1-4939-9084-9
Chien-Hung Lin, Michael Levin, Fiona J. Burnell, Generalized string-net models: A thorough exposition, Phys. Rev. B 103 (2021) 195155 [arXiv:2012.14424, doi:10.1103/PhysRevB.103.195155]
Constructing correlators in rational conformal field theory via string net models:
Constructing modular functors from pivotal bicategories using string net models:
Exposition and review:
Christoph Schweigert, String-net methods for CFT correlators, talk at QFT and Cobordism, CQTS (Mar 2023) [web]
Jürgen Fuchs, Christoph Schweigert, Simon Wood, Yang Yang, pp. 18 of: Algebraic structures in two-dimensional conformal field theory, Encyclopedia of Mathematical Physics [arXiv:2305.02773]
On the membrane analog related to the Yetter model for strict 2-groups:
Alex Bullivant, Clement Delcamp. Excitations in strict 2-group higher gauge models of topological phases (2019). (arXiv:1909.07937).
Clement Delcamp. Tensor network approach to electromagnetic duality in (3+1)d topological gauge models (2021). (arXiv:2112.08324).
Last revised on July 6, 2024 at 01:59:15. See the history of this page for a list of all contributions to it.