Efficient calculation of three-dimensional tensor networks

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant study of classical statistical models and (2+1)-dimensional quantum lattice models. In context a model, we determine partition function by solving dominant eigenvalue problem transfer matrix, whose left right eigenvectors are represented two projected entangled simplex states. These states not Hermitian conjugate each other but appropriately arranged so that their inner product can be computed much more efficiently than usual prescription. For Ising calculated internal energy spontaneous magnetization agree with published results literature. The possible improvement extension also discussed.