REVIEW 4 cited by
Dualities in one-dimensional quantum lattice models: topological sectors
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
abstract
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-$\frac{1}{2}$ Heisenberg XXZ model. One model has symmetry operators forming the fusion category $\mathsf{Rep}(\mathcal S_3)$ of representations of the group $\mathcal S_3$. We find that the mapping between its topological sectors and those of the XXZ model is associated with the non-trivial braided auto-equivalence of the Drinfel'd center of $\mathsf{Rep}(\mathcal S_3)$.
Forward citations
Cited by 4 Pith papers
-
Lattice non-invertible symmetry from non-commuting transfer matrices
For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
-
Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals
In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.
-
Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.
-
Les Houches Lecture Notes on Tensor Networks
A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.
Discussion (0). Sign in to comment.