  The novel concept of entanglement renormalization and its corresponding
tensor network renormalization technique have been highly successful in
developing a controlled real space renormalization group (RG) scheme.
Numerically approximate fixed-point (FP) tensors are widely used to extract the
conformal data of the underlying conformal field theory (CFT) describing
critical phenomena. In this paper, we present an explicit analytical
construction of the FP tensor for 2D rational CFT. We define it as a
correlation function between the "boundary-changing operators" on triangles.
Our construction fully captures all the real-space RG conditions. We also
provide a concrete example using the Ising model to compute the scaling
dimensions explicitly based on the corresponding FP tensor. Interestingly, our
construction of FP tensors is closely related to a strange correlator, where
the holographic picture naturally emerges. Our results also open a new door
towards understanding CFT in higher dimensions.
