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Walker-Wang model

Contents

Contents

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

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)

Last revised on May 23, 2021 at 04:46:51. See the history of this page for a list of all contributions to it.