nLab Walker-Wang model

Idea

The Walker-Wang model is a model (in theoretical physics) which is a 4d TQFT analog of the Levin-Wen model 3d TQFT. It is the Hamiltonian formulation of the TQFT whose partition function formulation is the Crane-Yetter model. It is speculated to have some application to topological insulators in solid state physics.

References

• 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)

Discussion of line defects and the loop braid group statistics, with application to topological phases of matter using higher gauge theory/higher parallel transport:

• C. W. von Keyserlingk, F. J. Burnell, Steven H. Simon, Three-dimensional topological lattice models with surface anyons, Phys. Rev. B 87, 045107 (arXiv:1208.5128, doi:10.1103/PhysRevB.87.045107)

• Alex Bullivant, Marcos Calcada, Zoltán Kádár, João Faria Martins, Paul Martin, Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry, Reviews in Mathematical Physics, Vol. 32, No. 04, 2050011 (2020) (arXi:1702.00868)

• AtMa P.O. Chan, Peng Ye, Shinsei Ryu, Braiding with Borromean Rings in (3+1)-Dimensional Spacetime, Phys. Rev. Lett. 121, 061601 (2018) [arXiv:1703.01926]

• Tian Lan, Liang Kong, Xiao-Gang Wen, A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons, Phys. Rev. X 8, 021074 (2018) (arXiv:1704.04221)

• Clement Delcamp, Excitation basis for (3+1)d topological phases, Journal of High Energy Physics 2017 (2017) 128 (arXiv:1709.04924 doi:10.1007/JHEP12(2017)128)

• Tian Lan, Xiao-Gang Wen, A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions, Phys. Rev. X 9, 021005 (2019) (arXiv:1801.08530)

• Alex Bullivant, João Faria Martins, Paul Martin, Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory, Advances in Theoretical and Mathematical Physics Volume 23 (2019) Number 7 (arXiv:1807.09551)

• Qing-Rui Wang, Meng Cheng, Chenjie Wang, Zheng-Cheng Gu, Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in (3+1)-Dimensions, Phys. Rev. B 99, 235137 (2019) (arXiv:1810.13428)

• Clement Delcamp, Apoorv Tiwari, On 2-form gauge models of topological phases, JHEP 05 (2019) 064 (arXiv:1901.02249)

With application to quantum computation:

• Sam Roberts, Stephen D. Bartlett, Symmetry-protected self-correcting quantum memories, Phys. Rev. X 10, 031041 (2020) (arXiv:1805.01474)

• Sam Roberts and Stephen D. Bartlett, Symmetry-Protected Self-Correcting Quantum Memories, Phys. Rev. X 10, 031041 2020 (doi:10.1103/PhysRevX.10.031041)

• Sam Roberts, Dominic J. Williamson, 3-Fermion topological quantum computation (arXiv:2011.04693)

• Charles Stahl, Rahul Nandkishore, Symmetry protected self correcting quantum memory in three space dimensions (arXiv:2103.08622)