REVIEW 7 cited by
On lattice models of gapped phases with fusion category symmetries
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 construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases. The construction is based on two-dimensional state sum TQFT whose input datum is an $H$-simple left $H$-comodule algebra, where $H$ is a finite dimensional semisimple Hopf algebra. We show that the actions of fusion category symmetries $\mathcal{C}$ on the boundary conditions of these state sum TQFTs are represented by module categories over $\mathcal{C}$. This agrees with the classification of gapped phases with symmetry $\mathcal{C}$. We also find that the commuting projector Hamiltonians for these state sum TQFTs have fusion category symmetries at the level of the lattice models and hence provide lattice realizations of gapped phases with fusion category symmetries. As an application, we discuss the edge modes of SPT phases based on these commuting projector Hamiltonians. Finally, we mention that we can extend the construction of topological field theories to the case of anomalous fusion category symmetries by replacing a semisimple Hopf algebra with a semisimple pseudo-unitary connected weak Hopf algebra.
Forward citations
Cited by 7 Pith papers
-
Algebraic locality and non-invertible Gauss laws
Non-invertible Gauss laws on lattices preserve Haag duality exactly only on cuspless regions; cusped regions require a collar, and group double models satisfy disjoint additivity.
-
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
-
SymTFT Approach for Mixed States with Non-Invertible Symmetries
A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.
-
Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d
Strange correlators and string order parameters for non-invertible SPT phases in 1+1d are systematically constructed from the interface algebra, giving local detectors of these phases.
-
Noninvertible Symmetry-Enriched Quantum Critical Point
A new class of gapless critical points in 1D, enriched by the noninvertible Rep(D8) symmetry, is constructed via the Kennedy-Tasaki duality and characterized by Ising and compact boson CFTs.
-
Higher Representations and Quark Confinement
Using higher-categorical representation theory, the paper proposes that the confined and adjoint Higgs phases of scalar QCD are distinguished by their baryon-charge spectra and by the presence of center vortices.
-
Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
Discussion (0). Continue with ORCID to comment.