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

TL;DR

This paper introduces two new truncation methods, SuperQ and iterative SuperQ, for the higher-order tensor renormalization group, improving the accuracy of tensor approximations in thermal equilibrium calculations.

Contribution

The paper proposes novel SuperQ and iterative SuperQ truncation schemes that minimize local errors and ensure consistent tensor mode projections in the tensor renormalization process.

Findings

SuperQ reduces local approximation errors effectively.

Iterative SuperQ further improves truncation accuracy.

Methods enhance the reliability of tensor network calculations.

Abstract

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