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Topological orders in 2+1d are spontaneous symmetry-breaking (SSB) phases of 1-form symmetries in pure states.
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1996
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Alexei Kitaev and John Preskill, “Topological entanglement entropy,” Physical Review Letters 96
2006
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Michael Levin and Xiao-Gang Wen, “Detecting topological order in a ground state wave function,” Physical Review Letters 96
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Claudio Castelnovo and Claudio Chamon, “Entanglement and topological entropy of the toric code at finite temperature,” Phys. Rev. B 76
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Alioscia Hamma, Claudio Castelnovo, and Claudio Chamon, “Toric-boson model: Toward a topological quantum memory at finite temperature,” Physical Review B 79
2009
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Steven T. Flammia, Alioscia Hamma, Taylor L. Hughes, and Xiao-Gang Wen, “Topological entanglement rényi entropy and reduced density matrix structure,” Phys. Rev. Lett. 103
2009
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Ayman Jarrous and Benny Pinkas, “Secure hamming distance based computation and its applications,” in Applied Cryptography and Network Security , edited by Michel Abdalla, David Pointcheval, Pierre-Alain Fouque, and Damien Vergnaud (Springer Berlin Heidelberg, Berlin, Heidelberg, 2009) pp. 107–124
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David Poulin, “Lieb-robinson bound and locality for general markovian quantum dynamics,” Phys. Rev. Lett. 104
2010
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Dimitris I. Tsomokos, Tobias J. Osborne, and Claudio Castelnovo, “Interplay of topological order and spin glassiness in the toric code under random magnetic fields,” Physical Review B 83
2011
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Matthew B. Hastings, “Topological order at nonzero temperature,” Phys. Rev. Lett. 107
2011
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Andrea Coser and David Pérez-García, “Classification of phases for mixed states via fast dissipative evolution,” Quantum 3
2019
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Tsung-Cheng Lu, Timothy H. Hsieh, and Tarun Grover, “Detecting topological order at finite temperature using entanglement negativity,” Physical Review Letters 125
2020
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Bruno Bertini, Pavel Kos, and Tomaz Prosen, “Operator entanglement in local quantum circuits i: Chaotic dual-unitary circuits,” SciPost Physics 8
2020
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2021
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Nick G. Jones, Julian Bibo, Bernhard Jobst, Frank Pollmann, Adam Smith, and Ruben Verresen, “Skeleton of matrix-product-state-solvable models connecting topological phases of matter,” Phys. Rev. Res. 3
2021
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Caroline de Groot, Alex Turzillo, and Norbert Schuch, “Symmetry Protected Topological Order in Open Quantum Systems,” Quantum 6
2022
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2022
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Hyukjoon Kwon, Rick Mukherjee, and M. S. Kim, “Reversing lindblad dynamics via continuous petz recovery map,” Physical Review Letters 128
2022
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2023
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Jian-Hao Zhang, Ke Ding, Shuo Yang, and Zhen Bi, “Fractonic higher-order topological phases in open quantum systems,” Physical Review B 108
2023
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Jong Yeon Lee, Chao-Ming Jian, and Cenke Xu, “Quantum criticality under decoherence or weak measurement,” PRX Quantum 4
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Yijian Zou, Shengqi Sang, and Timothy H. Hsieh, “Channeling quantum criticality,” Physical Review Letters 130
2023
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Guo-Yi Zhu, Nathanan Tantivasadakarn, Ashvin Vishwanath, Simon Trebst, and Ruben Verresen, “Nishimori’s cat: Stable long-range entanglement from finite-depth unitaries and weak measurements,” Physical Review Letters 131
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