nLab Zhenghan Wang

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Selected writings

On modular tensor categories:

• Eric Rowell, Richard Stong, Zhenghan Wang, On classification of modular tensor categories, Comm. Math. Phys. 292 (2009) no. 2, 343–389 (arXiv:0712.1377)

On braiding of su(2)-anyons providing universal quantum gates for topological quantum computation:

• Michael Freedman, Michael Larsen, Zhenghan Wang, A modular functor which is universal for quantum computation, Communications in Mathematical Physics 227 (2002) 605–622 [arXiv:quant-ph/0001108, doi:10.1007/s002200200645]

On topological quantum computation with anyons in Chern-Simons theory:

• Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38 (arXiv:quant-ph/0101025, doi:10.1090/S0273-0979-02-00964-3, pdf)

• Zhenghan Wang, Topological Quantum Computation, CBMS Regional Conference Series in Mathematics 112, AMS 2010 (ISBN-13: 978-0-8218-4930-9, pdf)

• Eric Rowell, Zhenghan Wang, Mathematics of Topological Quantum Computing, Bull. Amer. Math. Soc. 55 (2018), 183-238 (arXiv:1705.06206, doi:10.1090/bull/1605)

and with focus on abelian anyons in terms of modular tensor categories:

• Liang Wang, Zhenghan Wang, In and around Abelian anyon models, J. Phys. A: Math. Theor. 53 505203 (2020) (doi:10.1088/1751-8121/abc6c0)

and via linear representations of mapping class groups:

• Wade Bloomquist, Zhenghan Wang: On Topological Quantum Computing With Mapping Class Group Representations, J. Phys. A: Math. Theor. 52 (2019) 015301 [doi:10.1088/1751-8121/aaeea1, arXiv:1805.04622]

Indication that the effective abelian Chern-Simons theory describing the fractional quantum Hall effect has to be understood, in general, as a spin Chern-Simons theory:

• Zhenghan Wang on joint work with N. Read: Spin MTC and Fermionic QH States, talk at Workshop on Topological Phases in Condensed Matter 2008, University of Illinois (2008) [pdf, pdf]

More on anyons:

• Simon Trebst, Matthias Troyer, Zhenghan Wang, A. W. W. Ludwig, A short introduction to Fibonacci anyon models, Prog. Theor. Phys. Supp. 176 384 (2008) [arXiv:0902.3275, doi:10.1143/PTPS.176.384]

  (Fibonacci anyons)

• C. Gils, E. Ardonne, Simon Trebst, D. A. Huse, A. W. W. Ludwig, Matthias Troyer, Zhenghan Wang, Anyonic quantum spin chains: Spin-1 generalizations and topological stability, Phys. Rev. B 87 (2013), 235120 [doi:10.1103/PhysRevB.87.235120, arXiv:1303.4290]

On wreath products of a cyclic with a symmetric group as analogs of (anyon) braid groups in dimension $\gt 2$:

• Michael Freedman, Matthew B. Hastings, Chetan Nayak, Xiao-Liang Qi, Kevin Walker, Zhenghan Wang: Projective Ribbon Permutation Statistics: a Remnant of non-Abelian Braiding in Higher Dimensions, Phys. Rev. B 83 115132 (2011) [doi:10.1103/PhysRevB.83.115132, arXiv:1005.0583]

On identifying topological order via topological entanglement entropy of the ground state:

• Hong-Chen Jiang, Zhenghan Wang, Leon Balents, Identifying Topological Order by Entanglement Entropy, Nature Physics 8, 902-905 (2012) (arXiv:1205.4289)

Introducing the 4d TQFT Walker-Wang model:

• Kevin Walker, Zhenghan Wang, (3+1)-TQFTs and Topological Insulators, Frontiers of Physics volume 7, pages 150–159 (2012) (arXiv:1104.2632, doi:10.1007/s11467-011-0194-z)

On number theoretic aspects of modular tensor categories:

• Orit Davidovich, Tobias Hagge, Zhenghan Wang, On Arithmetic Modular Categories, arXiv preprit, 2013 [arXiv:1305.2229]

On Levin-Wen models:

• 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]

On braid group representations (specifically the Burau representation and its relation to the Alexander polynomial) and their application to topological quantum computation:

• Colleen Delaney, Eric C. Rowell, Zhenghan Wang, Local unitary representations of the braid group and their applications to quantum computing, Revista Colombiana de Matemáticas(2017), 50 (2):211 (arXiv:1604.06429, doi:10.15446/recolma.v50n2.62211)

A proposal for classifying symmetry-protected anyonic topological order in terms of 2-groupoidal-actions on modular tensor categories:

• Zhenghan Wang, §2.2 of: Beyond Anyons, Modern Physics Letters A 33 28 (2018) 1830011 [arXiv:1710.00464, doi:10.1142/S0217732318300112]

• Maissam Barkeshli, Parsa Bonderson, Meng Cheng, Zhenghan Wang, Symmetry Fractionalization, Defects, and Gauging of Topological Phases, Phys. Rev. B 100 115147 (2019) $[$arXiv:1410.4540, doi:10.1103/PhysRevB.100.115147, talk pdf$]$

On super-modular tensor categories:

• Parsa Bonderson, Eric C. Rowell, Qing Zhang, Zhenghan Wang: Congruence Subgroups and Super-Modular Categories, Pacific J. Math. 296 (2018) 257-270 [arXiv:1704.02041, doi:10.2140/pjm.2018.296.257]

Argument realizing anyonic topological order in the worldvolume-field theory on M5-branes via KK-compactification on closed 3-manifolds (Seifert manifolds) analogous to the 3d-3d correspondence (which instead uses hyperbolic 3-manifolds):

• Shawn X. Cui, Yang Qiu, Zhenghan Wang, From Three Dimensional Manifolds to Modular Tensor Categories, Commun. Math. Phys. 397 (2023) 1191–1235 [doi:10.1007/s00220-022-04517-4, arXiv:2101.01674]

On adiabatic transformations of certain 2d topological insulators:

• David Aasen, Zhenghan Wang, Matthew B. Hastings, Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes [arXiv:2203.11137]

Related entries

• Walker-Wang model

category: people