  We introduce a tensor renormalization group scheme for coarse-graining a
two-dimensional tensor network that can be successfully applied to both
classical and quantum systems on and off criticality. The key innovation in our
scheme is to deform a 2D tensor network into small loops and then optimize the
tensors on each loop. In this way, we remove short-range entanglement at each
iteration step and significantly improve the accuracy and stability of the
renormalization flow. We demonstrate our algorithm in the classical Ising model
and a frustrated 2D quantum model.
