A defect-network construction for modulated symmetries is derived, with an anomaly-free condition S*[ω]=[ω] that leads to classifications of dipolar and multipolar SPTs in 1+1D and 2+1D.
e 2πi N 2 gxphx`kx´rhx`kxsq (119) ωII “ e 2πi N 2 gQphx`kx´rhx`kxsq (120) whererg` hs denotes addition mod N and the subscript denotes the “type
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Defect Networks for Topological Phases Protected By Modulated Symmetries
A defect-network construction for modulated symmetries is derived, with an anomaly-free condition S*[ω]=[ω] that leads to classifications of dipolar and multipolar SPTs in 1+1D and 2+1D.