In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered. A theoretical contraction framework is therefore proposed. Furthermore, the canonical polyadic decomposition is introduced to tensor network theory. A lowest order numerical verification of this method on the 3-D Ising model is carried out.
Categories: cond-mat.stat-mech