Tensor RG Approach to High-Temperature Fixed Point

We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of RG maps have been quite successful at reproducing known critical behavior. In those numerical must be truncated to keep dimension legs tensors bounded. Our act on an infinite-dimensional Hilbert space, and our does not involve any truncations. has trivial fixed point which represents high-temperature point. prove if we start with is close this tensor, then iterates converge in Hilbert-Schmidt norm tensor. It important emphasize statement true simplest network one simply contracts four copies define renormalized The linearization simple about contraction due presence so-called CDL tensors. work provides first step towards problem rigorous neighborhood