String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
Symmetric entanglers for non-invertible SPT phases
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with $\mathrm{Rep}(A_4)$-symmetry, as a matrix product unitary (MPU).
fields
cond-mat.str-el 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.