nLab Xiao-Gang Wen

Xiao-Gang Wen is the BMO Financial Group Isaac Newton Chair in Theoretical Physics at Perimeter Institute. His expertise is in condensed matter theory of strongly correlated electronic systems and topological phases of matter. He introduced and studied the concept of topological order and its symmetry proteced versions.

• Institute page at MIT

• Wikipedia entry

Interview on topological order:

• Philip Ball, Making the world from topological order, National Science Review 6 2 (2019) 227–230 $[$doi:10.1093/nsr/nwy116$]$

Selected writings

Introducing and developing the notion of topological order:

• Xiao-Gang Wen, Vacuum Degeneracy of Chiral Spin State in Compactified Spaces, Phys. Rev. B 40 7387 (1989) [doi:10.1103/PhysRevB.40.7387]

• Xiao-Gang Wen, Topological Orders in Rigid States, Int. J. Mod. Phys. B 4 239 (1990) [doi:10.1142/S0217979290000139, pdf]

• Xiao-Gang Wen, Qian Niu: Ground state degeneracy of the FQH states in presence of random potential and on high genus Riemann surfaces, Phys. Rev. B 41 9377 (1990) [doi:10.1103/PhysRevB.41.9377]

• Xiao-Gang Wen, Non-Abelian statistics in the fractional quantum Hall states, Phys. Rev. Lett. 66 (1991) 802 (doi:10.1103/PhysRevLett.66.802)

• E. Keski-Vakkuri, Xiao-Gang Wen: Ground state structure of hierarchical QH states on torus and modular transformation, Int. J. Mod. Phys. B 7 4227 (1993) [doi:10.1142/S0217979293003644, arXiv:hep-th/9303155]

• Xiao-Gang Wen, Topological order and edge structure of $\nu = 1/2$ quantum Hall state, Phys. Rev. Lett. 70 (1993) 355 $[$doi:10.1103/PhysRevLett.70.355$]$

• Xiao-Gang Wen, Topological orders and Edge excitations in FQH states, Advances in Physics 44 (1995) 405 $[$arXiv:cond-mat/9506066v2, doi:10.1080/00018739500101566$]$

Early review:

• Xiao-Gang Wen, Topological orders and Chern-Simons theory in strongly correlated quantum liquid, International Journal of Modern Physics B 05 10 (1991) 1641-1648 [doi:10.1142/S0217979291001541]

Further review:

• Xiao-Gang Wen, Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89 41004 (2017) [arXiv:1610.03911, doi:10.1103/RevModPhys.89.041004]

On quantum spin liquids as exhibiting topological order:

• Xiao-Gang Wen, Frank Wilczek, Anthony Zee, Chiral spin states and superconductivity, Phys. Rev. B 39 (1989) 11413 [doi:10.1103/PhysRevB.39.11413]

The additional requirement that the Berry connection be non-abelian (and/or the presence of anyons):

• Zheng-Cheng Gu, Xiao-Gang Wen, p. 2 of: Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order, Phys. Rev. B 80 155131 (2009) $[$arXiv:0903.1069, doi:10.1103/PhysRevB.80.155131$]$

On understanding generalized Laughlin wavefunctions as conformal blocks:

• B. Blok, Xiao-Gang Wen, Many-body systems with non-abelian statistics, Nuclear Physics B 374 3 (1992) 615-646 $[$doi:10.1016/0550-3213(92)90402-W$]$

• Xiao-Gang Wen, Yong-Shi Wu, Chiral operator product algebra hidden in certain fractional quantum Hall wave functions, Nucl. Phys. B 419 (1994) 455-479 $[$doi:10.1016/0550-3213(94)90340-9$]$

Suggestion that topological order goes along with long-range entanglement:

• Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen, Section V of: Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order Phys. Rev. B 82 155138 (2010) $[$arXiv:1004.3835$]$

On the quantum adiabatic theorem in the context of topological phases of matter:

• Mathew B. Hastings, Xiao-Gang Wen, Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance, Phys. Rev. B 72 (2005) 045141 [arXiv:cond-mat/0503554, doi:10.1103/PhysRevB.72.045141]

Introducing string-net models and the Levin-Wen model:

• Michael Levin, Xiao-Gang Wen, String-net condensation: A physical mechanism for topological phases, Phys.Rev. B71 (2005) 045110 (arXiv:cond-mat/0404617)

Introducing the 3d toric code:

• Alioscia Hamma, Paolo Zanardi, Xiao-Gang Wen, String and Membrane condensation on 3D lattices, Phys. Rev. B72:035307, 2005 (arXiv:cond-mat/0411752, doi:10.1103/PhysRevB.72.035307)

Introducing topological entanglement entropy in view of string-net models:

• 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 the notion of symmetry protected topological phases:

• Zheng-Cheng Gu, Xiao-Gang Wen, Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order, Phys. Rev. B 80 155131 (2009) $[$arXiv:0903.1069, doi:10.1103/PhysRevB.80.155131$]$

On string-net models via tensor networks:

• 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$]$

On the classification of free fermion SPTs:

• Xiao-Gang Wen, Symmetry-protected topological phases in noninteracting fermion systems, Phys. Rev. B 85 (2012) 085103 $[$doi:10.1103/PhysRevB.85.085103$]$

On internal-symmetry protected topological phases:

• Peng Ye, Xiao-Gang Wen, Projective construction of two-dimensional symmetry-protected topological phases with $\mathrm{U}(1)$, $SO(3)$, or $SU(2)$ symmetries, Phys. Rev. B 87 195128 (2013) $[$doi:10.1103/PhysRevB.87.195128, arXiv:1212.2121$]$

Claim that group cohomology classifies some symmetry protected topological phases:

• Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Phys. Rev. B 87 (2013) 155114 $[$arXiv:1106.4772$]$

• Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, Xiao-Gang Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Science 338 (2012) 1604-1606 (arXiv:10.1103/PhysRevB.87.155114)

• Zheng-Cheng Gu, Xiao-Gang Wen, Symmetry-protected topological orders for interacting fermions – fermionic topological non-linear sigma-models and a group super-cohomology theory, Phys. Rev. B 90 115141 (2014) $[$arXiv:1201.2648, doi:10.1103/PhysRevB.90.115141$]$

More on topological order/topological phases of matter:

• Xiao-Gang Wen, Topological orders and edge excitations in FQH states, Advances in Physics 44, 405 (1995). cond-mat/9506066

• Xiao-Gang Wen, Vacuum degeneracy of chiral spin state in compactified spaces, Phys. Rev. B, 40, 7387 (1989),

• Xiao-Gang Wen, Topological orders in rigid states, Int. J. Mod. Phys. B4, 239 (1990)

• Xiao-Gang Wen, Qian Niu, Ground state degeneracy of the FQH states in presence of random potential and on high genus Riemann surfaces, Phys. Rev. B41, 9377 (1990)

• E. Keski-Vakkuri, Xiao-Gang Wen, Ground state structure of hierarchical QH states on torus and modular transformation, Int. J. Mod. Phys. B7, 4227 (1993) pdf

• Xiao-Gang Wen, Mean field theory of spin liquid states with finite energy gap and topological orders, Phys. Rev. B 44 2664 (1991).

• Xiao-Gang Wen, Non-Abelian Statistics in the FQH states, pdf Phys. Rev. Lett. 66, 802 (1991).

• Xiao-Gang Wen, Yong-Shi Wu, Chiral operator product algebra hidden in certain FQH states, Nucl. Phys. B419, 455 (1994), pdf

• Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen, Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order Phys. Rev. B 82, 155138 (2010)

• Juven Wang, Zheng-Cheng Gu, Xiao-Gang Wen, Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond, arxiv:1405.7689, Phys. Rev. Lett. 114, 031601 (2015)

• Liang Kong, Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang, Hao Zheng, Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry (arXiv:2005.14178)

On quantum information theory (entanglement entropy) applied to topological phases of matter/topological order:

• Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen:

  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$]$

Related entries

• topological order

• symmetry protected trivial order

• Levin-Wen model

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