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We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix.
A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathematical Physics 3
1972
Earlier work this paper cites.
M.-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications 10
1975
Earlier work this paper cites.
M. Den Nijs and K. Rommelse, Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains, Physical Review B 40
1989
Earlier work this paper cites.
T. Kennedy and H. Tasaki, Hidden z 2 × \times z 2 symmetry breaking in haldane-gap antiferromagnets, Physical review b 45
1992
Earlier work this paper cites.
H.-P. Breuer, F. Petruccione, et al. , The theory of open quantum systems (Oxford University Press on Demand, 2002)
2002
Earlier work this paper cites.
M. B. Hastings, Locality in quantum and markov dynamics on lattices and networks, Physical review letters 93
2004
Earlier work this paper cites.
R. Raussendorf, S. Bravyi, and J. Harrington, Long-range quantum entanglement in noisy cluster states, Physical Review A 71
2005
Earlier work this paper cites.
M. B. Hastings and T. Koma, Spectral gap and exponential decay of correlations, Communications in mathematical physics 265
2006
Earlier work this paper cites.
M. B. Hastings, An area law for one-dimensional quantum systems, Journal of statistical mechanics: theory and experiment 2007
2007
Earlier work this paper cites.
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quant. Inf. Comput. 7
2007
Earlier work this paper cites.
D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, String order and symmetries in quantum spin lattices, Physical review letters 100
2008
Earlier work this paper cites.
Z.-C. Gu and X.-G. Wen, Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order, Physical Review B 80
2009
Earlier work this paper cites.
2009
Earlier work this paper cites.
F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Physical review b 81
2010
Earlier work this paper cites.
M. Sanz, D. Perez-Garcia, M. M. Wolf, and J. I. Cirac, A quantum version of wielandt’s inequality, IEEE Transactions on Information Theory 56
2010
Earlier work this paper cites.
N. Schuch, D. Pérez-García, and I. Cirac, Classifying quantum phases using matrix product states and projected entangled pair states, Physical review b 84
2011
Earlier work this paper cites.
M. B. Hastings, Topological order at nonzero temperature, Physical review letters 107
2011
Earlier work this paper cites.
F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Symmetry protection of topological phases in one-dimensional quantum spin systems, Physical review b 85
2012
Earlier work this paper cites.
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry-protected topological orders in interacting bosonic systems, Science 338
2012
Earlier work this paper cites.
F. Pollmann and A. M. Turner, Detection of symmetry-protected topological phases in one dimension, Physical review b 86
2012
Earlier work this paper cites.
B. Buča and T. Prosen, A note on symmetry reductions of the lindblad equation: transport in constrained open spin chains, New Journal of Physics 14
2012
Cited alongside, same era.
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry protected topological orders and the group cohomology of their symmetry group, Physical Review B 87
2013
Cited alongside, same era.
G. De las Cuevas, N. Schuch, D. Pérez-García, and J. I. Cirac, Purifications of multipartite states: limitations and constructive methods, New Journal of Physics 15
2013
Cited alongside, same era.
V. V. Albert and L. Jiang, Symmetries and conserved quantities in lindblad master equations, Physical Review A 89
2014
Cited alongside, same era.
X. Chen, Y.-M. Lu, and A. Vishwanath, Symmetry-protected topological phases from decorated domain walls, Nature communications 5
2014
C. Zhu, T. Lan, and X.-G. Wen, Topological nonlinear σ \sigma -model, higher gauge theory, and a systematic construction of 3 + 1 D 3+1\text{D} topological orders for boson systems, Phys. Rev. B 100
2019
Later among the works it cites.
M. McGinley and N. R. Cooper, Fragility of time-reversal symmetry protected topological phases, Nature Physics 16
2020
Later among the works it cites.
M. Levin, Constraints on order and disorder parameters in quantum spin chains, Communications in Mathematical Physics 378
2020
Later among the works it cites.
S. Roberts and S. D. Bartlett, Symmetry-protected self-correcting quantum memories, Phys. Rev. X 10
2020
Later among the works it cites.
J. I. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Reviews of Modern Physics 93
2021
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Cited alongside, same era.
D. V. Else and C. Nayak, Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge, Physical Review B 90
2014
Cited alongside, same era.
T. Senthil, Symmetry-protected topological phases of quantum matter, Annu. Rev. Condens. Matter Phys. 6
2015
Cited alongside, same era.
G. De las Cuevas, T. Cubitt, J. I. Cirac, M. Wolf, and D. Pérez-García, Fundamental limitations in the purifications of tensor networks, Journal of Mathematical Physics 57
2016
Cited alongside, same era.
M. Cheng, M. Zaletel, M. Barkeshli, A. Vishwanath, and P. Bonderson, Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface, Physical Review X 6
2016
Cited alongside, same era.
D. J. Williamson, N. Bultinck, M. Mariën, M. B. Şahinoğlu, J. Haegeman, and F. Verstraete, Matrix product operators for symmetry-protected topological phases: Gauging and edge theories, Physical Review B 94
2016
Cited alongside, same era.
S. Roberts, B. Yoshida, A. Kubica, and S. D. Bartlett, Symmetry-protected topological order at nonzero temperature, Physical Review A 96
2017
Cited alongside, same era.
J. I. Cirac, D. Perez-Garcia, N. Schuch, and F. Verstraete, Matrix product density operators: Renormalization fixed points and boundary theories, Annals of Physics 378
2017
Cited alongside, same era.
Later among the works it cites.
M. B. Şahinoğlu, D. Williamson, N. Bultinck, M. Mariën, J. Haegeman, N. Schuch, and F. Verstraete, Characterizing topological order with matrix product operators, Annales Henri Poincaré 22
2021
Later among the works it cites.
P. Sompet, S. Hirthe, D. Bourgund, T. Chalopin, J. Bibo, J. Koepsell, P. Bojović, R. Verresen, F. Pollmann, G. Salomon, et al. , Realizing the symmetry-protected haldane phase in fermi–hubbard ladders, Nature 606
2022
Later among the works it cites.
D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, et al. , A quantum processor based on coherent transport of entangled atom arrays, Nature 604
2022
Later among the works it cites.
C. de Groot, A. Turzillo, and N. Schuch, Symmetry protected topological order in open quantum systems, Quantum 6
2022
Later among the works it cites.
2022
Later among the works it cites.
R. Ma and C. Wang, Average symmetry-protected topological phases, Physical Review X 13
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
2023
Later among the works it cites.
Y.-H. Chen and T. Grover, Separability transitions in topological states induced by local decoherence, Physical Review Letters 132
2024
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