Altland-Zirnbauer Tenfold Way
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Tenfold Way (Altland-Zirnbauer 1997, Kitaev 2009): All gapped fermionic Hamiltonians fall into exactly 10 symmetry classes, determined by three discrete symmetries: Time-reversal T (T²=0,±1), Particle-hole C (C²=0,±1), and their product sublattice symmetry S=TC. Each class has a specific topological classification (Z, Z₂, or 0) in each spatial dimension, forming a periodic table of topological phases.