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Emergent Hamiltonians from gauging boundary symmetries
Specialist level
Speaker:
José Garre
Institution:
IFT
Location&Place:
Grey Room 3
Abstract:
We propose a systematic framework to construct (d+1)-dimensional local and commuting Hamiltonians from an initial generic d-dimensional abelian symmetry. We do so by gauging iteratively the d-dim symmetry which introduces gauge fields endowed with the dual symmetry that can be gauged again. The emergent Hamiltonian is given by the resulting local symmetries, the modified 'Gauss law', of the iterative gauging process, i.e. it is a stabilizer code.
We first show that by iterating the gauging of Abelian group symmetries on spin chains and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizers of the XZZX-code, equivalent to the toric code, for any Abelian group. Our construction naturally realizes any gapped boundary by taking the different quantum phases of an initial (1+1)D globally symmetric system and resembles a 'lattice SymTFT'.
Next we showcase our paradigm by constructing three-dimensional surface codes from iteratively gauging a global 0-form, and its dual 1-form, symmetry that lives in two dimensions. We additionally provide two more examples in d=2 in which different type-I fracton orders emerge from gauging initial linear subsystem and Sierpinski fractal symmetries.
This is based on
J. Garre-Rubio, 'Emergent (2+1)D topological orders from iterative (1+1)D gauging', Nature Commun. 15, 7986 (2024)
B Vancraeynest-De Cuiper, J. Garre-Rubio, 'Systematic construction of stabilizer codes via gauging abelian boundary symmetries', arXiv: 2410.09044
J. Garre-Rubio, 'Emergent (2+1)D topological orders from iterative (1+1)D gauging', Nature Commun. 15, 7986 (2024)
B Vancraeynest-De Cuiper, J. Garre-Rubio, 'Systematic construction of stabilizer codes via gauging abelian boundary symmetries', arXiv: 2410.09044
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