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The quantum anomaly of a global symmetry is known to strongly constrain the allowed low-energy physics in a clean and isolated quantum system.
Two soluble models of an antiferromagnetic chain
Elliott Lieb, Theodore Schultz, and Daniel Mattis · 1961
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Axial-vector vertex in spinor electrodynamics
Stephen L Adler · 1969
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A pcac puzzle: π 0 → γ γ \pi^{0}\rightarrow\gamma\gamma in the σ \sigma -model
John Stewart Bell and Roman W Jackiw · 1969
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Linear transformations which preserve trace and positive semidefiniteness of operators
Andrzej Jamiołkowski · 1972
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Random-field instability of the ordered state of continuous symmetry
Yoseph Imry and Shang-keng Ma · 1975
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking
G’t Hooft · 1980
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Order parameter for spin-glasses
Giorgio Parisi · 1983
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Percolation, quantum tunnelling and the integer hall effect
JT Chalker and PD Coddington · 1988
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Rounding of first-order phase transitions in systems with quenched disorder
Michael Aizenman and Jan Wehr · 1989
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Rounding effects of quenched randomness on first-order phase transitions
Michael Aizenman and Jan Wehr · 1990
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Quantum percolation and plateau transitions in the quantum hall effect
Dung-Hai Lee, Ziqiang Wang, and Steven Kivelson · 1993
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Random antiferromagnetic quantum spin chains
Daniel S Fisher · 1994
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Topological approach to luttinger’s theorem and the fermi surface of a kondo lattice
Masaki Oshikawa · 2000
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Lieb-schultz-mattis in higher dimensions
Matthew B Hastings · 2004
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Quantum criticality beyond the landau-ginzburg-wilson paradigm
T Senthil, Leon Balents, Subir Sachdev, Ashvin Vishwanath, and Matthew PA Fisher · 2004
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Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
Matthew B Hastings and Xiao-Gang Wen · 2005
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Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
Zheng-Cheng Gu and Xiao-Gang Wen · 2009
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Rounding of first order transitions in low-dimensional quantum systems with quenched disorder
Rafael L Greenblatt, Michael Aizenman, and Joel L Lebowitz · 2009
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Matthew B Hastings · 2010
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Interplay of topological order and spin glassiness in the toric code under random magnetic fields
Dimitris I Tsomokos, Tobias J Osborne, and Claudio Castelnovo · 2011
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Symmetry-protected topological orders in interacting bosonic systems
Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen · 2012
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Topology, delocalization via average symmetry and the symplectic anderson transition
Liang Fu and Charles L Kane · 2012
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Braiding statistics approach to symmetry-protected topological phases
Michael Levin and Zheng-Cheng Gu · 2012
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Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems
Michael Aizenman, Rafael L Greenblatt, and Joel L Lebowitz · 2012
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Symmetry protected topological orders and the group cohomology of their symmetry group
Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen · 2013
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Boson topological insulators: A window into highly entangled quantum phases
Chong Wang and T Senthil · 2013
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Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
Dominic V Else and Chetan Nayak · 2014
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Anomalies of discrete symmetries in various dimensions and group cohomology
Anton Kapustin and Ryan Thorngren · 2014
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Symmetry-protected topological phases from decorated domain walls
Xie Chen, Yuan-Ming Lu, and Ashvin Vishwanath · 2014
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Universal scaling of the quantum anomalous hall plateau transition
Jing Wang, Biao Lian, and Shou-Cheng Zhang · 2014
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All-fermion electrodynamics and fermion number anomaly inflow
Shauna Kravec, John McGreevy, and Brian Swingle · 2015
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Anomalous symmetry fractionalization and surface topological order
Xie Chen, Fiona J Burnell, Ashvin Vishwanath, and Lukasz Fidkowski · 2015
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Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators
Max A Metlitski, CL Kane, and Matthew PA Fisher · 2015
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Anderson localization and the topology of classifying spaces
Takahiro Morimoto, Akira Furusaki, and Christopher Mudry · 2015
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Construction of bosonic symmetry-protected-trivial states and their topological invariants via g × s o ( ∞ ) g\times so(\infty) nonlinear σ \sigma models
Xiao-Gang Wen · 2015
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Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond
Juven C Wang, Zheng-Cheng Gu, and Xiao-Gang Wen · 2015
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From trivial to topological paramagnets: The case of ℤ 2 \mathbb{Z}_{2} and ℤ 2 3 \mathbb{Z}_{2}^{3} symmetries in two dimensions
Maxime Dupont, Snir Gazit, and Thomas Scaffidi · 2021
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Discrete theta angles, symmetries and anomalies
Po-Shen Hsin and Ho Tat Lam · 2021
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Strange correlation function for average symmetry-protected topological phases
Jian-Hao Zhang, Yang Qi, and Zhen Bi · 2022
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Symmetry protected topological phases under decoherence
Jong Yeon Lee, Yi-Zhuang You, and Cenke Xu · 2022
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Lieb-schultz-mattis, luttinger, and’t hooft-anomaly matching in lattice systems
Meng Cheng and Nathan Seiberg · 2023
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The “parity” anomaly on an unorientable manifold
Edward Witten · 2016
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Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface
Meng Cheng, Michael Zaletel, Maissam Barkeshli, Ashvin Vishwanath, and Parsa Bonderson · 2016
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Classification and properties of symmetry-enriched topological phases: Chern-simons approach with applications to z 2 spin liquids
Yuan-Ming Lu and Ashvin Vishwanath · 2016
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Anomaly manifestation of lieb-schultz-mattis theorem and topological phases
Gil Young Cho, Chang-Tse Hsieh, and Shinsei Ryu · 2017
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Anomaly indicators for time-reversal symmetric topological orders
Chenjie Wang and Michael Levin · 2017
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Theta, time reversal and temperature
Davide Gaiotto, Anton Kapustin, Zohar Komargodski, and Nathan Seiberg · 2017
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8d gauge anomalies and the topological green-schwarz mechanism
Iñaki García-Etxebarria, Hirotaka Hayashi, Kantaro Ohmori, Yuji Tachikawa, and Kazuya Yonekura · 2017
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Average symmetry-protected topological phases
Ruochen Ma and Chong Wang · 2023
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Reviving the lieb-schultz-mattis theorem in open quantum systems
Yi-Neng Zhou, Xingyu Li, Hui Zhai, Chengshu Li, and Yingfei Gu · 2023
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Anomalies of average symmetries: Entanglement and open quantum systems
Po-Shen Hsin, Zhu-Xi Luo, and Hao-Yu Sun · 2023
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Quantum criticality under decoherence or weak measurement
Jong Yeon Lee, Chao-Ming Jian, and Cenke Xu · 2023
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Topological phases with average symmetries: the decohered, the disordered, and the intrinsic
Ruochen Ma, Jian-Hao Zhang, Zhen Bi, Meng Cheng, and Chong Wang · 2023
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Pivot hamiltonians as generators of symmetry and entanglement
Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, and Ruben Verresen · 2023
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Building models of topological quantum criticality from pivot hamiltonians
Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, and Ruben Verresen · 2023
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Exactly solvable model for a deconfined quantum critical point in 1d
Carolyn Zhang and Michael Levin · 2023
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Diagnostics of mixed-state topological order and breakdown of quantum memory
Ruihua Fan, Yimu Bao, Ehud Altman, and Ashvin Vishwanath · 2023
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Yimu Bao, Ruihua Fan, Ashvin Vishwanath, and Ehud Altman · 2023
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Higher-form symmetries under weak measurement
Kaixiang Su, Nayan Myerson-Jain, Chong Wang, Chao-Ming Jian, and Cenke Xu · 2023
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Mixed-state quantum phases: Renormalization and quantum error correction
Shengqi Sang, Yijian Zou, and Timothy H Hsieh · 2023
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Bulk-boundary correspondence for intrinsically gapless symmetry-protected topological phases from group cohomology
Rui Wen and Andrew C. Potter · 2023
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Gauging lie group symmetry in (2+ 1) d topological phases
Meng Cheng, Po-Shen Hsin, and Chao-Ming Jian · 2023
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Gapped boundary of (4+ 1) d beyond-cohomology bosonic spt phase
Xinping Yang and Meng Cheng · 2023
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Lieb-schultz-mattis theorem in open quantum systems
Kohei Kawabata, Ramanjit Sohal, and Shinsei Ryu · 2024
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Mixed-state quantum anomaly and multipartite entanglement
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