REVIEW 5 cited by
Gapless topological phases and symmetry-enriched quantum criticality
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 introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the $1+1d$ case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the former is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking Ising phase. An example of the latter arises between the gapped Ising and cluster phases: this symmetry-enriched Ising CFT has an edge mode with finite-size splitting $\sim 1/L^{14}$. In addition to such new cases, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer -- including a complete characterization of symmetry-enriched $1+1d$ Ising CFTs. Non-trivial topological invariants can also be constructed in higher dimensions, which we illustrate for a symmetry-enriched $2+1d$ CFT without gapped sectors.
Forward citations
Cited by 5 Pith papers
-
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.
-
Topological Transition on the Conformal Manifold
Fermionic conformal field theories on a line of couplings can pair up so that opposite sides differ by an invertible topological order, a continuous topological transition that maps to Kramers-Wannier duality after bo...
-
Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
At a critical point of a PT-symmetric non-Hermitian SSH chain, the biorthogonal entanglement entropy scales logarithmically with central charge c=-2, attributed to a bc-ghost non-unitary CFT.
-
Organizing transitions and their cascades: Generalized symmetry enforcement in massless flows or Higgs transitions
The unbroken fusion ring symmetry FR(SU(2)_{p-2}) stabilizes the massless RG flow M(p,p+1)->M(p-1,p) by making every invariant IR primary field irrelevant.
-
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.