Symmetry actions on hidden quantum Markov models for 1D spin systems are classified by group-cohomology 2-cocycles, yielding a stochastic description of SPT order that matches the AKLT chain.
Physical Review B85, 075125 (2012)
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Cocycle Actions on Hidden Quantum Markov Models: Symmetry Protection and Topological Order
Symmetry actions on hidden quantum Markov models for 1D spin systems are classified by group-cohomology 2-cocycles, yielding a stochastic description of SPT order that matches the AKLT chain.