More is different.
God is in the details.
- 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）
- Automatic structural optimization of tree tensor networks
- Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, and Tomotoshi Nishino
- 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.
- 11 pages, 10 figures, 2 tables
- Neural Network Approach to Scaling Analysis of Critical Phenomena
- Ryosuke Yoneda and Kenji Harada
- 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.
- 10 pages, 9 figures
- Aug 26, 2022
- Conference (invited talk)
- The 15th Asia Pacific Physics Conference (APPC15), Korea (online)
- Tensor renormalization group study of the non-equilibrium critical fixed point of the one-dimensional contact process
- 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.