An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase

M. Freedman and Matthew B Hastings, “Classification of quantum cellular automata,” (2019), arXiv:1902.10285

Original

1902

Earlier work this paper cites.

Lukasz Fidkowski, Jeongwan Haah, Matthew B Hastings, and Nathanan Tantivasadakarn, “Disentangling the generalized double semion model,” (2019), arXiv:1906.04188

Original

1906

Earlier work this paper cites.

Jeongwan Haah, “Clifford quantum cellular automata: Trivial group in 2d and Witt group in 3d,” (2019), arXiv:1907.02075

Original

1907

Earlier work this paper cites.

Clay Córdova, Kantaro Ohmori, Shu-Heng Shao, and Fei Yan, “Decorated ℤ 2 \mathbb{Z}_{2} symmetry defects and their time-reversal anomalies,” (2019), arXiv:1910.14046

Original

1910

Earlier work this paper cites.

Michael Freedman, Jeongwan Haah, and Matthew B. Hastings, “The group structure of quantum cellular automata,” arXiv:1910.07998

Original

1910

Earlier work this paper cites.

Robbert Dijkgraaf and Edward Witten, “Topological gauge theories and group cohomology,” Communications in Mathematical Physics 129

1990

Earlier work this paper cites.

Louis Crane, Louis H Kauffman, and David N Yetter, “State-sum invariants of 4-manifolds,” Journal of Knot Theory and Its Ramifications 6

1997

Earlier work this paper cites.

Frank Verstraete and J Ignacio Cirac, “Mapping local hamiltonians of fermions to local hamiltonians of spins,” Journal of Statistical Mechanics: Theory and Experiment 2005

2005

Earlier work this paper cites.

A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics 321

2006

Earlier work this paper cites.

Matthew B Hastings, “Solving gapped hamiltonians locally,” Physical Review B 73

2006

Earlier work this paper cites.

Sergey Bravyi, Matthew Hastings, and Spyridon Michalakis, “Topological quantum order: Stability under local perturbations,” J. Math. Phys. 51

Original

2010

Earlier work this paper cites.

Kevin Walker and Zhenghan Wang, “(3+1)-TQFTs and topological insulators,” Frontiers of Physics 7

Original

2011

Earlier work this paper cites.

Michael Levin and Zheng-Cheng Gu, “Braiding statistics approach to symmetry-protected topological phases,” Phys. Rev. B 86

Original

2012

Cited alongside, same era.

D. Gross, V. Nesme, H. Vogts, and R. F. Werner, “Index theory of one dimensional quantum walks and cellular automata,” Communications in Mathematical Physics 310

Original

2012

Cited alongside, same era.

Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group,” Phys. Rev. B 87

Original

2013

Cited alongside, same era.

Jeongwan Haah, “Commuting Pauli hamiltonians as maps between free modules,” Commun. Math. Phys. 324

Original

2013

Cited alongside, same era.

Lukasz Fidkowski, Xie Chen, and Ashvin Vishwanath, “Non-abelian topological order on the surface of a 3D topological superconductor from an exactly solved model,” Phys. Rev. X 3

Xie Chen, F. J. Burnell, Ashvin Vishwanath, and Lukasz Fidkowski, “Anomalous symmetry fractionalization and surface topological order,” Phys. Rev. X 5

Original

2015

Later among the works it cites.

Xie Chen and Michael Hermele, “Symmetry fractionalization and anomaly detection in three-dimensional topological phases,” Phys. Rev. B 94

Original

2016

Later among the works it cites.

Daniel S. Freed and Michael J. Hopkins, “Reflection positivity and invertible topological phases,” (2016), arXiv:1604.06527

Original

2016

Later among the works it cites.

Michael H. Freedman and Matthew B. Hastings, “Double semions in arbitrary dimension,” Communications in Mathematical Physics 347

Original

2016

Later among the works it cites.

Nicolas Tarantino and Lukasz Fidkowski, “Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases,” Phys. Rev. B 94