Speaker
Description
Abstract
We introduce a systematic framework to obtain emergent local, commuting Hamiltonians in (d+1) dimensions from abelian symmetries living on a d-dimensional boundary. Starting from a generic d-dim globally symmetric system, we iteratively gauge its abelian symmetry, thereby introducing layers of gauge fields carrying dual symmetries that can themselves be gauged again. The fixed points of this iterative gauging procedure define (d+1)-dim stabilizer Hamiltonians from the local “Gauss law” constraints encoding the emergent bulk order while realizing the original symmetry in the boundary. It will be explained how this construction in 1D reproduces familiar 2D topological codes such as the toric code model, and naturally realizes all gapped boundary conditions as different 1D symmetric phases at the boundary. The framework, akin to a lattice SymTFT construction, is extended to higher-form and subsystem symmetries in any dimension, yielding for example to foliated and fractal type-I fracton 3D models.