Nuclear norm regularized loop optimization for tensor network

TL;DR

This paper introduces a nuclear norm regularized loop optimization method for tensor networks, improving stability and accuracy in tensor renormalization, especially for critical 2D Ising models.

Contribution

The proposed algorithm incorporates nuclear norm regularization into loop optimization, effectively avoiding local minima and enhancing tensor network renormalization performance.

Findings

Achieves higher accuracy in scale invariance of renormalized tensors.

Provides more stable extraction of higher scaling dimensions.

Outperforms standard methods in critical 2D Ising model simulations.

Abstract

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical 2D Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion.