Topological aspects of the critical three-state Potts model
- URL: http://arxiv.org/abs/2107.11177v2
- Date: Tue, 22 Mar 2022 12:03:51 GMT
- Title: Topological aspects of the critical three-state Potts model
- Authors: Robijn Vanhove, Laurens Lootens, Hong-Hao Tu, Frank Verstraete
- Abstract summary: A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT to the lattice setting.
The symmetries are represented by matrix product operators (MPO), as well as intertwiners between the diagonal tetracritical Ising model and the non-diagonal three-state Potts model.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We explore the topological defects of the critical three-state Potts spin
system on the torus, Klein bottle and cylinder. A complete characterization is
obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d
rational CFT to the lattice setting. This is done by applying the strange
correlator prescription to the recently obtained tensor network descriptions of
string-net ground states in terms of bimodule categories [Lootens, Fuchs,
Haegeman, Schweigert, Verstraete, SciPost Phys. 10, 053 (2021)]. The symmetries
are represented by matrix product operators (MPO), as well as intertwiners
between the diagonal tetracritical Ising model and the non-diagonal three-state
Potts model. Our categorical construction lifts the global transfer matrix
symmetries and intertwiners, previously obtained by solving Yang-Baxter
equations, to MPO symmetries and intertwiners that can be locally deformed,
fused and split. This enables the extraction of conformal characters from
partition functions and yields a comprehensive picture of all boundary
conditions.
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