Tensor renormalization group centered about a core tensor

We propose a modified form of tensor renormalization-group algorithm for evaluating partition functions of classical statistical mechanical models on two-dimensional lattices. This algorithm coarse-grains only the rows and columns of the lattice adjacent to a single core tensor at each step, such that the lattice size shrinks linearly with the number of coarse-graining steps as opposed to shrinking exponentially as in the usual tensor renormalization group (TRG). However, the cost of this approach only scales as O(chi(4)) in terms of the bond dimension chi, significantly cheaper than the O(chi(6)) cost scaling of TRG, whereas numerical benchmarking indicates that both approaches have comparable accuracy for the same bond dimension chi. It follows that the algorithm can allow for more accurate investigation of classical models on modestly sized lattices than is possible with standard TRG.