Recent developments in non-invertible symmetry-preserving quantum lattice models allow access to many 2D CFTs, and RG flows among them. Density matrix renormalization group (DMRG), on the other hand, allows us to study these lattice models super efficiently. I will explain our recent work on combining these methods to study the coupled tricritical Ising model, in search of irrational CFTs. If time permits, I will also discuss the RG flow connecting different conformal interfaces between the Ising CFT and the tricritical Ising CFT.