Towards topological fixed-point models beyond gappable boundaries

Understand

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks.

• Such zero-correlation length models with an exact notion of topological invariance are known in the mathematical community as state-sum constructions or lattice topological quantum field theories.
• All of the established ansatzes for fixed-point models imply the existence of a gapped boundary as well as a commuting-projector Hamiltonian.
• Thus, they fail to capture topological phases without a gapped boundary or commuting-projector Hamiltonian, most notably chiral topological phases in $2+1$ dimensions.