REVIEW 3 cited by
Twisted Quantum Double Model of Topological Orders with Boundaries
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a three-cocycle in the third cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a two-cochain in the second cochain group of $K$ over $U(1)$. The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the two-cochain given the three-cocyle. We offer a closed-form formula computing the ground state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wavefunction of the model on a disk also in terms of the input data only.
Forward citations
Cited by 3 Pith papers
-
Planar fault-tolerant circuits for non-Clifford gates on the 2D color code
The paper constructs a family of planar fault-tolerant 'twisted color circuits' that implement logical T gates and magic-state measurements on the 2D color code via a path-integral and color-cohomology framework.
-
Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization
A string-net framework constructs exactly solvable SET lattice models from intrinsic categorical symmetries, including a nonabelian S3-enriched example whose gauging produces the S4 quantum-double phase.
-
Handbook of Error-Correcting Codes
The paper compiles a curated handbook reference of error-correcting codes, their symbol-based classifications, and interrelations with mathematical objects and physical phases.
Discussion (0). Continue with ORCID to comment.