A lattice construction of the Kormos-Runkel-Watts defect flows in minimal models
Abstract
Kormos, Runkel, and Watts (KRW) showed that a topological defect of a diagonal minimal model M(p,p+1), perturbed by a weakly relevant defect field, flows to a new conformal interface. We study the flow of the (2,1) Verlinde defect D(2,1) driven by the spinful defect field ϕ(1,3)⊗ϕ̅(3,3) on the lattice. The flow preserves the (r,1) Verlinde lines. This preserved symmetry makes a dilute RSOS realisation possible. We study this flow numerically using both exact diagonalization and density matrix renormalization group (DMRG). At p=4, the flow ends on the invertible line η=D(3,1). At p=5 it ends on a non-trivial conformal interface C5 with g=1.503(2) and transmission coefficient T=0.665(10). We report its spectrum, leading irrelevant dimension, and lattice β-function. Gauging η maps C5 to an interface of the three-state Potts model, which breaks ℤ3 but is a stable interface once the Fibonacci line τFib and charge conjugation are imposed. A loop-model formulation allows us to follow the family Cp at continuous 4≤ p≤5: it moves smoothly from C5 to η as we lower p.
Related
- Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality
- Emergent Andreev Reflection from a Lattice Duality Defect
- Construction of holomorphic SCFTs with minimal index
- Physical reduced states and continuum characters of the lattice Kramers-Wannier defect
- Scalable construction of force-constant basis sets for large-scale anharmonic lattice-dynamical calculations
BibTeX
@misc{rong2026lattice,
title = {{A lattice construction of the Kormos-Runkel-Watts defect flows in minimal models}},
author = {Junchen Rong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03824},
eprint = {2611.03824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03824},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A lattice construction of the Kormos-Runkel-Watts defect flows in minimal models
AU - Junchen Rong
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03824
UR - https://arxiv.org/abs/2611.03824
AB - Kormos, Runkel, and Watts (KRW) showed that a topological defect of a diagonal minimal model M(p,p+1), perturbed by a weakly relevant defect field, flows to a new conformal interface. We study the flow of the (2,1) Verlinde defect D_(2,1) driven by the spinful defect field ϕ_(1,3)⊗ϕ̅_(3,3) on the lattice. The flow preserves the (r,1) Verlinde lines. This preserved symmetry makes a dilute RSOS realisation possible. We study this flow numerically using both exact diagonalization and density matrix renormalization group (DMRG). At p=4, the flow ends on the invertible line η=D_(3,1). At p=5 it ends on a non-trivial conformal interface C_5 with g=1.503(2) and transmission coefficient T=0.665(10). We report its spectrum, leading irrelevant dimension, and lattice β-function. Gauging η maps C_5 to an interface of the three-state Potts model, which breaks ℤ_3 but is a stable interface once the Fibonacci line τ_Fib and charge conjugation are imposed. A loop-model formulation allows us to follow the family C_p at continuous 4≤ p≤5: it moves smoothly from C_5 to η as we lower p.
ER -