Topological phases with generalized global symmetries
By B. Yoshida. 2015
136 citations recorded by the source corpus.
We present simple lattice realizations of symmetry-protected topological phases with q-form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d+1)-colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/99b14d3cc2534c466729cc6bc1332d7250d4315b
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In Artificial Intelligence
- Nathanan Tantivasadakarn
- Ashvin Vishwanath
- N. G. Jones
- Frank Pollmann
- D. Parker
- R. Verresen
- Romain Vasseur
- Ryan Thorngren
In Atomic and Molecular Physics, and Optics
- Ryan Thorngren
- R. Verresen
- Ashvin Vishwanath
- Romain Vasseur
- Nathanan Tantivasadakarn
- D. Parker
- N. G. Jones
- Thomas Scaffidi
Citations in the corpus
- Generalized Symmetries in Condensed Matter (2022, unknown): “Lattice models for higher-form SPTs have been written down in (62, 63) and effective theories studied in (64).”
- Gapless Symmetry-Protected Topological Order (2017, methodology): “To set the notation, we first recall the construction of a gapped SPT with Z2×Z2 symmetry in one dimension [30, 43, 63, 69], which is closely related to the experimentally observable Haldane phase [31, 70, 71].”
- Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “Similarly the B1B2 SPT (RBH cluster state) [97, 153, 154] has stabilizers 0 0 0 0 x̄(1 + z̄) x̄(1 + ȳ)”
- Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, methodology): “[121] Beni Yoshida, “Topological phases with generalized global symmetries,” Phys.”