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Topological edge and interface states at bulk disorder-to-order quantum critical points

Topological edge and interface states at bulk disorder-to-order quantum critical points

We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of $3d$ bulk disorder-to-order phase transitions. We then generalize our study to $2d$ gapless states localized at an …