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We extend the periodic table of phases of free fermions in the ten-fold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry $\hat G$ in an arbitrary dimension.
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Q-R. Wang, Z-C. Gu, “Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory,” Phys. Rev. X 8
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