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Consider the partition function of a classical system in two spatialdimensions, or the Euclidean path integral of a quantum system in twospace-time dimensions, both on a lattice. We show that the tensor networkrenormalization (TNR) algorithm [\emph{G. Evenbly and G. Vidal, Phys. Rev.Lett. 115, 180405}] can be used to implement local scale transformations onthese objects, namely a lattice version of conformal maps. Specifically, weexplain how to implement the lattice equivalent of the logarithmic conformalmap that transforms the Euclidean plane into a cylinder. As an application, andwith the 2D critical Ising model as a concrete example, we use this map tobuild a lattice version of the scaling operators of the underlying conformalfield theory, from which one can extract their scaling dimensions and operatorproduct expansion coefficients.

Local scale transformations on the lattice with tensor network renormalization