REVIEW 4 cited by
An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
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 an exactly solvable commuting projector model for a $4+1$ dimensional ${\mathbb Z}_2$ symmetry-protected topological phase (SPT) which is outside the cohomology classification of SPTs. The model is described by a decorated domain wall construction, with "three-fermion" Walker-Wang phases on the domain walls. We describe the anomalous nature of the phase in several ways. One interesting feature is that, in contrast to in-cohomology phases, the effective ${\mathbb Z}_2$ symmetry on a $3+1$ dimensional boundary cannot be described by a quantum circuit and instead is a nontrivial quantum cellular automaton (QCA). A related property is that a codimension-two defect (for example, the termination of a ${\mathbb Z}_2$ domain wall at a trivial boundary) will carry nontrivial chiral central charge $4$ mod $8$. We also construct a gapped symmetric topologically-ordered boundary state for our model, which constitutes an anomalous symmetry enriched topological phase outside of the classification of arXiv:1602.00187, and define a corresponding anomaly indicator.
Forward citations
Cited by 4 Pith papers
-
Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata
On a 3+1d cubic lattice, the duality (gauging) and 1-form-SPT-stacking operations generate local automorphisms whose fusion rules match the continuum only up to translations and non-trivial QCAs — semion, 3-fermion, a...
-
Quantum Cellular Automata on Symmetric Subalgebras
Quantum cellular automata on finite-Abelian-symmetric subalgebras of 1D spin chains are completely classified by an anyon-permutation invariant and a generalized GNVW index.
-
Bosonic SPT and invertible phases and its relation to Steenrod's problem
Bosonic beyond-cohomology SPT phases are governed by a mod-3 Steenrod-power differential, and a new 6+1-dimensional Z3×Z3 Dijkgraaf-Witten phase is nontrivial on simplicial complexes but trivial on manifolds.
-
Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
Discussion (0). Continue with ORCID to comment.