Finite-size and finite bond dimension effects of tensor network renormalization

We propose a general procedure for extracting the running coupling constants of underlying field theory given classical statistical model on two-dimensional lattice, combining tensor network renormalization (TNR) and finite-size scaling conformal theory. By tracking at each scale, we are able to visualize group flow demonstrate it with Ising three-state Potts models. Furthermore, utilizing this methodology, reveal limitations due finite bond dimension $D$ TNR applied critical systems. find that correlation length is imposed by in TNR, can be attributed an emergent relevant perturbation respects symmetries system. The shows same power-law dependence as ``finite entanglement scaling'' matrix product states.