日本物理学会　2022年秋季大会（東京工業大学）

日程: 2020年9月12日から9月15日

• 講演(13pH113-5) "ネットワーク構造最適化を含んだツリーテンソルネットワーク法の開発" （共同研究者：引原俊哉, 上田宏, 奥西巧一, 西野友年）
• 講演(13pH113-6) "テンソルネットワーク状態を用いた教師なし生成モデルのネットワーク構造の最適化" （共同研究者：大久保毅, 川島直輝）
• 講演(13pH113-8) "GPUによる2次元MERAの変分最適化の加速" （共同研究者：真鍋秀隆）
• 講演(14pH112-1) "行列積状態を用いたテンソル化深層学習における最適ランクの推定" （共同研究者：阿蘇品侑雅）

Title

Automatic structural optimization of tree tensor networks

Author

Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, and Tomotoshi Nishino

Abstract

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground-state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.

Comments

11 pages, 10 figures, 2 tables

Preprint

arXiv:2209.03196

Title

Neural Network Approach to Scaling Analysis of Critical Phenomena

Author

Ryosuke Yoneda and Kenji Harada

Abstract

Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. As methods for determining this universality class from data, polynomial regression, which is less accurate, and Gaussian process regression, which provides high accuracy and flexibility but is computationally heavy, have been proposed. In this paper, we propose a method by a regression method using a neural network. The computational complexity is only linear in the number of data points. We demonstrate the proposed method for the finite-size scaling analysis of critical phenomena on the two-dimensional Ising model and bond percolation problem to confirm the performance. This method efficiently obtains the critical values with accuracy in both cases.

Comments

10 pages, 9 figures

Preprint

arXiv:2209.01777

Date

Aug 26, 2022

Conference (invited talk)

The 15th Asia Pacific Physics Conference (APPC15), Korea (online)

Title

Tensor renormalization group study of the non-equilibrium critical fixed point of the one-dimensional contact process

Abstract

The steady-state of many stochastic systems is non-equilibrium. We studied the phase of non-equilibrium systems and the transition similar to equilibrium systems. In particular, the critical phase transition is interesting because we can define the non-equilibrium universality class. To confirm the existence of a non-equilibrium critical fixed point, we study the time evolution operator of one-dimensional contact processes by using a tensor renormalization group technique. The time evolution operators converge to universal critical tensors in the tensor renormalization group flow. The spectrums of critical tensors are strongly anisotropic but share the intrinsic structure each for the universality class. The integer structure for the universality class of compact-directed percolation in the time direction is consistent with the exact spectrum structure of the diffusion-annihilation process.

日本物理学会　2022年年次大会

日程: 2020年3月15日から3月19日（オンライン開催）

• 講演(16aE11-4) "テンソルネットワーク近似を用いたランダム量子回路サンプリングの古典シミュレーション" （共同研究者：真鍋秀隆）
• 講演(15aB12-9) "ニューラルネットワークを用いたスケーリング解析手法" （共同研究者：米田亮介，発表は原田）

新型コロナウイルス感染症への対応として、年次大会はオンライン開催になりました。

数理科学2022年2月号No.704：テンソルネットワークの進展（多彩な表現形式が物理をつなぐ）に解説記事「テンソルネットワーク入門」を寄稿。