Global optimization of tensor renormalization group using the corner transfer matrix

Understand

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed.

• Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration is unnecessary, which is a time-consuming part of other methods with global optimization.
• In addition, a further approximation reducing the order of the computational cost of contraction for the calculation of the coarse-grained tensor is proposed.
• The computational time of our algorithm in two dimensions scales as the sixth power of the bond dimension while the higher-order tensor renormalization group and the higher-order second renormalization group methods have the seventh power.