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

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