Initial tensor construction for the tensor renormalization group

TL;DR

This paper introduces a systematic method for constructing initial tensor networks for the tensor renormalization group, improving the accuracy and efficiency of physical property calculations without sign problems.

Contribution

It presents a novel approach to translate general tensor representations into suitable initial tensors for TRG, enhancing algorithm performance.

Findings

The method enables more accurate initial tensor construction for TRG.

Improved TRG algorithms show better convergence and stability.

The approach reduces dependence on initial tensor choices.

Abstract

We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network representations of physical quantities to investigate physical properties without encountering the sign problem. To apply the TRG, it is essential to construct a locally connected tensor network suitable for recursive coarse-graining. We present a systematic approach for translating a general tensor representation of the partition function to this form. Furthermore, we show the dependence of TRG algorithms on the choice of the initial tensor network representation and propose an improvement of TRG algorithms in this respect