Improved local truncation schemes for the higher-order tensor renormalization group method

The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical quantum systems in thermal equilibrium. At every step iterative blocking procedure, coarse-grid truncated to keep dimension under control. For consistent it crucial that forward backward modes are projected on same lower dimensional subspaces. In this paper we present two methods, SuperQ method, construct truncations reduce or even minimize local approximation errors, while satisfying constraint.