A lattice construction of the Kormos-Runkel-Watts defect flows in minimal models

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 $ϕ_{(1,3)}\otimes\barϕ_{(3,3)}$ 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 $\mathbb{Z}_3$ but is a stable interface once the Fibonacci line $τ_{\mathrm{Fib}}$ and charge conjugation are imposed. A loop-model formulation allows us to follow the family $C_p$ at continuous $4\le p\le5$: it moves smoothly from $C_5$ to $η$ as we lower $p$.