## ARCHIVES

• 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.
11 pages, 10 figures, 2 tables
Preprint
arXiv:2209.03196

Title
Neural Network Approach to Scaling Analysis of Critical Phenomena
Author
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.
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.

• 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）

We will hold the oneline workshop, Tensor Network States: Algorithms and Applications (TNSAA) 2021-2022, from Jan. 17 to Jan. 21, 2022. The series of workshop, TNSAA, has been organized for the purposes of exchanging new developments, having discussions toward future studies, and providing intruductory talks for new generation of researchers about tensor networks.

• 講演(21aL3-3) "吸収状態相転移の非平衡臨界点における普遍的スペクトラム構造のテンソル繰り込み群による研究"
• 講演(22pL4-9) "行列積表現を用いたニューラルネットワークのエンタングルメント解析" (共同研究者) 阿蘇品 侑雅（発表）
• 講演(23pA1-1) "テンソルネットワークを用いた量子回路学習" (共同研究者) 真鍋 秀隆（発表）

Date
May 31, 2021
Seminar
StatPhys seminar at University of Tokyo, Hongo, Japan
Title
Universal spectrum structure on the nonequilibrium critical line of the one-dimensional Domany-Kinzel cellular automaton
Abstract
The Domany-Kinzel(DK) cellular automaton is a stochastic time-evolutional system with an absorbing state from which the system cannot escape and a canonical model for nonequilibrium critical phenomena[1]. We introduce the tensor network method as a new tool to study it. Estimating the entropy of the DK automaton with a matrix product state representation of distribution, we reported a new cusp of the Renyi entropy in the active phase of the DK cellular automaton[2]. We recently applied a tensor renormalization group method to transfer matrices at the nonequilibrium critical point of the DK cellular automaton, confirming a universal spectrum structure[3]. In this talk, we will report our results with a brief review of models and methods.

[1] M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions. Volume 1: Absorbing Phase Transitions, Vol. 1 (Springer, 2008).
[2] K. H. and N. Kawashima, Entropy Governed by the Absorbing State of Directed Percolation, Physical Review Letters 123, 090601 (2019).
[3] K. H., Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation, arXiv:2008.10807.

• 講演(14pL2-3) "テンソルネットワーク状態の幾何学的変換"

Title
Critical exponents in coupled phase-oscillator models on small-world networks
Reference
Physical Review E 102, 062212 (2020)
DOI
10.1103/PhysRevE.102.062212
Author
Ryosuke Yoneda, Kenji Harada, and Yoshiyuki Y. Yamaguchi
Abstract
A coupled phase-oscillator model consists of phase oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the nonsynchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a small-world network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in small-world networks irrespective of the order of links. Our numerical results suggest that the number of universality classes is reduced to one and the critical exponent is shared in the considered models having coupling functions up to second harmonics with unimodal and symmetric natural frequency distributions.
8 pages, 8 figures
Preprint
arXiv:2007.04539

• 講演(9pL1-9) "スモールワールドネットワーク上の結合位相振動子系における同期転移の臨界指数" （共同研究者）米田亮介(発表者), 山口義幸
• 講演(10pL2-7) "同時有向浸透現象の相転移"（共同研究者）星野佑樹(発表者)
• 講演(10pL2-8) "臨界有向浸透現象のスペクトラムを用いた新しい普遍性の提案"

Preprint
arXiv:2008.10807
Author
Abstract
Using a tensor renormalization group method with oblique projectors for an anisotropic tensor network, we confirm that the rescaled spectrum of transfer matrices at nonequilibrium critical points in the (1+1)-dimensional directed percolation, a canonical model of nonequilibrium critical phenomena, is scale-invariant and its structure is universal.
6 pages, 7 figures

Preprint
arXiv:2007.04539
Title
Critical exponents in coupled phase-oscillator models on small-world networks
Author
Ryosuke Yoneda, Kenji Harada, Yoshiyuki Y. Yamaguchi
Abstract
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of models is widely studied since it describes the synchronization transition, which emerges between the non-synchronized state and partially synchronized states, and which is characterized by the critical exponents. Among them, we focus on the critical exponent defined by coupling strength dependence of the order parameter. The synchronization transition is not limited in the all-to-all interaction, whose number of links is of O(N2) with N oscillators, and occurs in small-world networks whose links are of O(N). In the all-to-all interaction, values of the critical exponent depend on the natural frequency distribution and the coupling function, classified into an infinite number of universality classes. A natural question is in small-world networks, whether the dependency remains irrespective of the order of links. To answer this question we numerically compute the critical exponent on small-world networks by using the finite-size scaling method with coupling functions up to the second harmonics and with unimodal and symmetric natural frequency distributions. Our numerical results suggest that, for the continuous transition, the considered models share the critical exponent 1/2, and that they are collapsed into one universality class.
7 pages, 7 figures

Title
Finite-m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
Reference
Physical Review E 101, 062111 (2020)
DOI
10.1103/PhysRevE.101.062111
Author
Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
Abstract
We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyzes for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension m at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sine-Gordon model.
7 pages, 7 figures
Preprint
arXiv:2001.10176

• 講演(18pK43-4) "テンソルネットワーク中のエンタングルメント最適化"
• 講演(19aPS-90) "Double DKセルオートマトンにおける相転移現象"（共同研究者）星野佑樹(発表者)

トヨタ自動車株式会社と京都大学との産学連携の新しい取組みである「モビリティ基盤数理」研究ユニットに参加し、 テンソルデータ解析に統計物理学的視点を導入するための共同研究をスタート。

Preprint
arXiv:2001.10176
Author
Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Roman Krčmár, Andrej Gendiar, Seiji Yunoki, and Tomotoshi Nishino
Abstract
We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyzes for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension m at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the c=1 boundary conformal field theory associated with the effective Z_6 dual sine-Gordon model.
7 pages, 7 figures

「テンソルネットワークによるセルオートマトンの状態確率分布の時間発展シミュレーション」, 日本シミュレーション学会誌「シミュレーション」2019年12月 Vol.38 No.4 page 228-231.

• Conference: Tensor Network States: Algorithms and Applications (TNSAA) 2019-2020
• Invited talk: "New numerical approaches for directed percolation"
• Date: Dec. 4, 2019
• Conference dates: Dec. 4-6, 2019
• Venue: NCCU, Taipei, TAIWAN
• URL：https://tnsaa7.github.io

• 開講日時
• 10月28日（月）4,5限（午後2時45分開始、午後6時終了）
• 10月29日（火）4,5限（午後2時45分開始、午後6時終了）
• 11月5日（火）4,5限（午後2時45分開始、午後6時終了）
• 11月6日（水）3限（午後1時開始、午後2時30分終了）
• 開講場所：京都大学　吉田キャンパス　総合研究8号館　講義室3（3階南）Map (No.59)。11月6日は講義室4（3階北）。
• 講義の概要・目的

相互作用する多数の要素からなる系（多体系）は多くの分野で見られるが、単純な相互作用であっても数学的に厳密な取り扱いは困難であることが多い。そのため、近年、コンピュータの進化と共に多体系向けの数値的手法は欠かせない基礎技術となってきている。この講義の目的は現在活発に開発が行なわれている多体系向けの数値的手法の総括を行うことで、それらに関する進んだ知識を取得することにある。

• 到達目標：多体系向けの数値的手法に関する基本的事項を理解した上で、各分野の問題に取り組める応用力の習得を目指す。
• 講義計画と内容：以下の内容を講述する。講義の進度に応じて省略する項目もある。
1. 多体系の例：時間発展系、平衡系、量子系、最適化問題、ベイズ推定
2. モンテカルロ法の基礎
3. モンテカルロ法のアルゴリズム：動的モンテカルロ法、ギブスサンプラー、メトロポリス法、量子モンテカルロ法、ハミルトニアンモンテカルロ法
4. テンソル分解とテンソルネットワークの基礎
5. テンソルネットワーク法のアルゴリズム
6. まとめと展望

なお、講義は京都大学情報学研究科の大学院生対象ですが、興味ある方はどなたでも参加して頂いて結構です。

• 講演(11aK25-9) "斜交射影を用いたテンソル繰り込み群によるセルオートマトンシミュレーション"（共同研究者）鉈落佳奈(発表者)
• 講演(11aK25-10) "強く非等方的な臨界点における不変性"
• 講演(13aPS-6) "セルオートマトンにおける全エントロピーのモンテカルロ計算"（共同研究者）星野佑樹(発表者), 鉈落佳奈

• 日程：２０１９年７月１６日（火） ～ ２０１９年８月８日（木）（４週間弱）
• 開催場所：東京大学物性研究所 (〒277−8581 柏市柏の葉5−1−5)
• ワークショップURL：http://www.issp.u-tokyo.ac.jp/public/caqmp2019/

TITLE
Entropy Governed by the Absorbing State of Directed Percolation
REFERENCE
Physical Review Letters 123, 090601 (2019)
DOI
10.1103/PhysRevLett.123.090601
AUTHOR
ABSTRACT
We investigate the informational aspect of (1+1)-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the “absorbing” state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Rényi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-order Rényi entropy has a clear cusp. There we also detect a singular behavior of “entanglement entropy,” defined by regarding the probability distribution as a wave function. The entanglement entropy vanishes below the singular point and stays finite above. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time evolution of the Rényi entropy at the critical point as well as in the active phase.

• 日程：２０１９年７月１６日（火） ～ ２０１９年８月８日（木）（４週間弱）
• 開催場所：東京大学物性研究所 (〒277−8581 柏市柏の葉5−1−5)
• URL：http://www.issp.u-tokyo.ac.jp/public/caqmp2019/
• 参加登録締切は6月28日（宿泊、旅費援助については：4月12日）。
• 参加登録ページはこちら
• キーワード：テンソルネットワーク、量子モンテカルロ法、フラストレートスピン系、トポロジカル量子相、情報統計、データ解析、機械学習、高エネルギー物理、実験、...

• 講演(14aG214-8) "角転送行列繰り込み群の有限状態数スケーリングを用いたBKT転移の評価"
（共同研究者）上田宏(理研R-CCS)(発表者), 奥西巧一(新潟大学), Roman Krcmar, Andrej Gendiar(スロバキア科学アカデミー), 柚木清司(理研R-CCS), 西野友年(神戸大学)
• 講演(15aG214-6) "吸収状態に支配される有向浸透現象のエントロピー" （共同研究者）川島直輝 (プレプリント: arXiv:1902.10479)
• 講演(17aS-PS-64) "有向浸透現象におけるエントロピーのモンテカルロ計算"（共同研究者）星野佑樹(発表者)

Session K19: Precision Many Body Physics VII on APS March Meeting 2019 (Boston, Massachusetts, USA)." date: 2019-03-06 lang: all category: News, Talk

March 4–8, 2019, Boston, Massachusetts, USA

PREPRINT: arXiv:1902.10479

Preprint
arXiv:1902.10479
Author
Abstract
We investigate the informational aspect of (1+1)-dimensional directed percolation(DP), a canonical model of a non-equilibrium continuous transition to a phase dominated by a single special state called the "absorbing" state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of DP. We find a universal relaxation of Renyi entropy at the absorbing phase transition point and a new singularity in the active phase where the second-order Renyi entropy has a cusp and the dynamical behavior of entanglement entropy changes from asymptotically-complete disentanglement to finite entanglement. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time-evolution of the Renyi entropy at the critical point as well as in the active phase.
6(=4+1.5) pages, 8(=5+3) figures

• タイトル：「(1+1)次元有向浸透現象のエントロピー」
• 日程：２０１８年１２月１７日(月)
• 場所：東京大学　6階大講義室／柏キャンパス
• シンポジウム日程：２０１８年１２月１７日(月) ～ １８日(火)
• シンポジウムWebページ：https://ccms.issp.u-tokyo.ac.jp/event/688

• Title: "Entropy of the (1+1)-dimensional directed percolation"
• Conference: International Conference on Advances in Physics of Emergent orders in Fluctuations (APEF2018)
• Conference dates: November 12-15, 2018
• Venue: The University of Tokyo, Tokyo, JAPAN
• URL：https://apef2018.org

• 開講日時
• 10月15日 3,4,5コマ（午後1時開始）
• 10月22日 3,4,5コマ（午後1時開始）
• 10月29日 3,4コマ（午後1時開始）
• 開講場所：京都大学　吉田キャンパス　総合研究8号館　講義室1（1階南）Map (No.59)
• 講義の概要・目的

相互作用する多数の要素からなる系（多体系）は多くの分野で見られるが、単純な相互作用であっても数学的に厳密な取り扱いは困難であることが多い。そのため、近年、コンピュータの進化と共に多体系向けの数値的手法は欠かせない基礎技術となってきている。この講義の目的は現在活発に開発が行なわれている多体系向けの数値的手法の総括を行うことで、それらに関する進んだ知識を取得することにある。

• 到達目標：多体系向けの数値的手法に関する基本的事項を理解した上で、各分野の問題に取り組める応用力の習得を目指す。
• 講義計画と内容：以下の内容を講述する。講義の進度に応じて省略する項目もある。
1. 多体系の例：時間発展系、平衡系、量子系、最適化問題、ベイズ推定
2. モンテカルロ法の基礎
3. モンテカルロ法のアルゴリズム：動的モンテカルロ法、ギブスサンプラー、メトロポリス法、量子モンテカルロ法、ハミルトニアンモンテカルロ法
4. テンソル分解とテンソルネットワークの基礎
5. テンソルネットワーク法のアルゴリズム
6. まとめと展望

なお、講義は京都大学情報学研究科の大学院生対象ですが、興味ある方はどなたでも参加して頂いて結構です。

• 講演(9aM302-1) "エントロピーを用いた(1+1)次元有向浸透現象の動的過程の特徴付け"、9月9日午前9時、領域11：非平衡揺らぎ
• ポスター講演(12aPS-96) "テンソルネットワークによる有向浸透現象の数値的研究"、9月12日午前10時、領域11：ポスターセッション（発表者：鉈落佳奈）

タイトル: "エンタングルメント分岐とその活用"
• 日時: 2018年8月1日午後2時半
• 会議名: 物性研短期研究会「量子情報・物性の新潮流」
• 会議日程: 2018年8月1日から2018年8月3日（3日間）
• 開催場所: 東京大学柏キャンパス　東京大学物性研究所　大講義室（千葉県柏市）
• URL: http://www.qi.t.u-tokyo.ac.jp/workshop/NQuIC2018/index.html

• 講演："1次元確率過程のテンソルネットワークシミュレーション"
• 日程：２０１８年７月１９日(木) ～ ２０日(金)
• 場所：東京大学　小柴ホール／本郷キャンパス
• 研究会Webページ：https://ccms.issp.u-tokyo.ac.jp/event/246

• 講演："有向浸透臨界現象におけるエントロピーから見たユニバーサリティクラス"
• 日程：４月２日(月) ～ ３日(火)
• 場所：東京大学物性研究所 6階 大講義室
• 研究会Webページ：http://ccms.issp.u-tokyo.ac.jp/events/eventsfolder/keisan18

• 講演(24pK604-6) "テンソルネットワークを用いた1次元非平衡モデルの時間発展シミュレーション"、3月24日午後、領域11：統計力学基礎論2・非平衡揺らぎ

Session S34: Precision Many Body Physics IV on APS March Meeting 2018 (Los Angeles, California, USA)." date: 2018-03-08 lang: all category: News, Talk

March 5–9, 2018, Los Angeles, California, USA.

Reference: Physical Review B 97 (2018) 045124.

REFERENCE Physical Review B 97 (2018) 045124
DOI 10.1103/PhysRevB.97.045124
ABSTRACT We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Wei-Lin is a student in a doctoral course of National Taiwan University. His stay is financially supported by Japan-Taiwan Exchange Association.

International Symposium on Fluctuation and Structure out of Equilibrium 2017 (SFS2017)
• Date of poster presentation: 14:50 ~ 16:50, 20th Nov. 2017.
• Conference: International Symposium on Fluctuation and Structure out of Equilibrium 2017
• Conference dates: From 20th Nov. 2017 to 23th Nov. 2017.
• Venue: Sendai International Center, Sendai, Japan.
• URL：http://sfs-dynamics.jp/sfs2017/

Title: "Entanglement branching operator" (invited)
• Date of presentation: 14:00 ~ 15:00, 6th Nov. 2017.
• Conference: Novel Quantum States in Condensed Matter 2017
• Conference dates: From 23th Oct. 2017 to 24th Nov. 2017.
• Venue: Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan.
• URL：http://www2.yukawa.kyoto-u.ac.jp/~nqs2017.ws/index.php
Preprint
arXiv:1710.01830
Abstract
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Preprint
arXiv:1710.01830
Author
Abstract
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.
9 pages, 11 figures

• 講演 "エンタングルメント分岐を用いたテンソル繰り込み群", 24aJ25-10

• 講演："エンタングルメント分岐を用いたテンソル繰り込み群"
• 日程：７月１１日(火) ～ １２日(水)
• 場所：東京大学　小柴ホール／本郷キャンパス
• 研究会Webページ：http://post-k.cms-initiative.jp/events/sympo20170711

• 講演 "繰り込み群とテンソルネットワーク" 18pB11-3、
領域11、領域3、素粒子論領域合同シンポジウム
「テンソルネットワーク法とその可能性」
• （共同研究者 伊井海生 発表）講演 "非平衡系のための数値的手法の開発" 19pK-PS-50
• （共同研究者 佐藤龍己 発表）講演 "有向浸透現象の数値的手法の開発" 19pS-PS-27
• （共同研究者 正木晶子 発表）講演 "並列化量子モンテカルロ法によるrelevant fieldを含む有限サイズスケーリング" 20aB11-7

From 5 Feb. 2017 to 18 Feb. 2017, Workshop "Entanglement in Strongly Correlated Systems" , the Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain.

• Title: "General Entanglement Branching in a Tensor Network" (invited)
• Date of presentation: 14th Dec. 2016.
• Conference: Fourth Workshop on Tensor Network States: Algorithms and Applications
• Conference dates: From 12th Dec. 2016 to 15th Dec. 2016.
• Venue: National Center for Theoretical Sciences, Hsinchu, Taiwan
• URL：http://www.phys.cts.nthu.edu.tw/actnews/index.php?Sn=318

9月13日から9月16日、

• 講演 "SU(N)一般化ハイゼンベルグモデルの量子相転移：Conformal bootstrap法の結果との比較、SO(5)対称性の検証" 13aAF-9

ポスト「京」萌芽的課題

キックオフミーティングに参加。

2016年度の京都大学オープンキャンパスで、研究室紹介を2回行う。テーマは、 "シミュレーションの最先端＋スパコン「京」"。主に、スパコン「京」で行っ ている大規模シミュレーションを紹介する予定。

• 日程：２０１６年６月２７日（月） ～ ２０１６年７月１５日（金）（３週間）
• 開催場所：東京大学物性研究所 (〒277−8581 柏市柏の葉5−1−5)
• URL：http://www.issp.u-tokyo.ac.jp/public/tnqmp2016/

3月19日から3月22日、

• 講演 "分岐とテンソルネットワーク" 20pBT-5

2016年3月16日(水) 15:00~、早稲田大学早稲田キャンパス３号館203号室、
Quantum Computation and Machine Learning Seminar Seriesにて講演。

（後半の内容は、新潟大学理学部 奥西巧一さんとの共同研究の成果です）

[1] K. Okunishi and K. Harada, Phys. Rev. B 89, 134422 (2014).
[2] K. Harada and K. Okunishi, unpublished (2016).

2016年1月29日（金）、 講演　”シミュレーションで探る量子の世界：絶対零度での秩序と臨界現象”、 スパコン「京」がひらく社会と科学　シンポジウム「スーパーコンピュータの今とこれから」、 よみうり大手町ホール（東京）。

• 日程：２０１６年６月２７日（月） ～ ２０１６年７月１５日（金）（３週間）
• 開催場所：東京大学物性研究所 (〒277−8581 柏市柏の葉5−1−5)
• URL（参加登録）：http://www.issp.u-tokyo.ac.jp/public/tnqmp2016/

date: 2016-01-25 lang: en category: News, Conf

Tensor network is a new language for talking about many-body problems. Having emerged from quantum information description of simple wave functions, it is now regarded as an extremely precise method for computing partition functions of classical or quantum lattice models, a wave function describing novel quantum states, a new framework of real-space renormalization group, a representation manifesting hidden symmetries and orders, a cure to the notorious negative-sign problem, a systematic way of information compression, a computable representation of AdS/CFT correspondence, ...

The main objective of this workshop is to achieve a better understanding of tensor-network states and tensor-network methods in quantum many-body problems. Related physical systems and numerical methods will be also discussed.

• 日程：１月１１日(月) ～ １４日(木)
• 場所：分子科学研究所　岡崎カンファレンスホール
• 研究会Webページ：http://qm.ims.ac.jp/tnsaa2016/

Web 理化学研究所 計算科学研究機構 広報誌「計算科学の世界」
PDF 理化学研究所 計算科学研究機構 広報誌「計算科学の世界」No.11

REFERENCE Physical Review B 92 (2015) 134404
DOI 10.1103/PhysRevB.92.134404
AUTHOR Tsuyoshi Okubo, Kenji Harada, Jie Lou, and Naoki Kaishima
ABSTRACT The SU(N) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two- dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at N = 10, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for N >= 15. This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

9月16日から9月19日、

REFERENCE Physical Review E 92 (2015) 012106
DOI 10.1103/PhysRevE.92.012106
ABSTRACT Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.
NOTE The reference code of this new method is prepared at http://kenjiharada.github.io/BSA/

5月25日から5月26日、 チュートリアル講演 "量子フラストレート磁性体のテンソルネットワークを用いた数値的研究"、 第32回量子情報技術研究会 (QIT32)、大阪大学。

BSAツールキットは臨界現象のスケーリング解析を行う新手法の参照コードです。ベイズ推定の力を用いて、自動的に臨界点や臨界指数を求めることができます。スケーリング補正を考慮した場合（オプション"-f 1"）のスケーリング関数の推定結果の出力部分にあるバグを訂正しました。このバグはパラメータの推定結果には影響はありません。

PREPRINT arXiv:1504.05332
AUTHOR Tsuyoshi Okubo, Kenji Harada, Jie Lou, Naoki Kaishima
ABSTRACT The SU(N) symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the N'eel order disappears at N = 10 indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the N'eel and the valence-bond solid ordering for N >= 15. This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the N'eel state, because the expected spontaneous order is too weak to be detected.

3月21日から3月24日、

• シンポジウム講演 "二次元SU(N)ハイゼンベルグモデルにおける脱閉じ込め量子臨界現象" 22aAL-4
• （共同研究者 吉田天平）講演 "ダイマーモット絶縁体における電荷揺らぎの解析" 24aAB-9

REFERENCE Physical Review B 91 (2015) 094414
DOI 10.1103/PhysRevB.91.094414
AUTHOR Takafumi Suzuki, Kenji Harada, Haruhiko Matsuo, Synge Todo, and Naoki Kaishima
ABSTRACT We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical XY model with a Z4 symmetry-breaking field and the three-state Potts model, respectively. In the square-lattice case, the thermal exponent, ν, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, η and γ/ν, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the Z4 symmetry-breaking field is always marginal. In contrast, ν in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the Z3 field remains relevant in the SU(3) and SU(4) cases.

Title: ''Quantum Monte Carlo study of Quantum Criticality on SO(N) Bilinear-biquadratic Chains''
Date: Feb. 18, 2015
Conference: From Feb. 18, 2015 to Feb. 21, 2015, International Workshop on New Frontier of Numerical Methods for Many-Body Correlations ― Methodologies and Algorithms for Fermion Many-Body Problems , Hongo Campus, The University of Tokyo, Japan.

Title: ''Quantum Monte Carlo study of Quantum Criticality on SO(N) Bilinear Biquadratic Chains''
Date: Jan. 9, 2015
Conference: From Jan. 7, 2015 to Jan. 11, 2015, the 9th International Conference on Computational Physics (ICCP9) , National University of Singapore, Singapore.

タイトル:「MERAテンソルネットワークを用いた量子多体系の計算手法」

YITP短期研究会 "量子多体系研究の新しい潮流 --テンソルネットワーク・繰り込み群・エンタングルメント--"に参加。

ポスター講演： 2014年12月9日（火）"カーネル法を用いた臨界現象の有限サイズスケーリング法とその応用"

Conference: 10sor network workshop --- Field 2x5 joint workshop on new algorithms for quantum manybody problems ---
Date: November 25, 2014, Tuedsay
Venue: Kashiwa Future Center, Kashiwa, Chiba, Japan
Title: "MERA tensor network and its application on quantum frustrated magnets"

From Nov. 4, 2014 to Dec. 2, 2014, the YITP long-term Workshop "Novel Quantum States in Condensed Matter 2014" (NQS2014) , YITP, Kyoto university, Kyoto, Japan.

ポスター講演： 2014年11月13日（木）"Kernel Method for Scaling Analysis of Critical Phenomena and its Implementation"

From 20 Oct. 2014 to 22 Oct. 2014, the CMSI International Workshop 2014: Tensor Network Algorithms in Materials Science , RIKEN Advanced Institute for Computational Science 6F auditorium 7-1-26, Port Island South, Kobe, 650-0047, Japan.

ツールキット BSAに新アプリケーション"new_bfss"を追加。臨界現象の有限サイズスケーリングにスケーリング補正を考慮した解析も行う新手法の参照コードです。カーネル法を用いて簡単に臨界点や臨界指数を求めることができます。

PREPRINT arXiv:1410.3622
ABSTRACT Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

９月７日から９月１０日、

• 講演 "有限サイズスケーリング補正のカーネル法" 10aAY-6
• 講演 （共同研究者）"一般化Jordan-Wigner変換とZ2xZ2対称性" 10pAQ-4
• 講演 "SO(N) bilinear-biquadratic スピン鎖の量子臨界性とストリング秩序の数値的研究" 10pAQ-5

• 主催：CMSI第1部会
• 日程：8月18日(月) ～ 22日(金)
• 場所：滋賀県高島市安曇川町近江白浜

REFERENCE JPS Conf. Proc. 3 , 014031 (2014) [7 pages]
Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)
DOI 10.7566/JPSCP.3.014031
ABSTRACT We will introduce tensor network states in the variational calculation of ground states for quantum frustrated magnets. In particular, we will report the performance of MERA tensor network for an S = 1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts.

date: 2014-06-26 lang: all category: News, Conf

From 25 to 27 June 2014, the ISSP International Workshop, "New Horizon of Strongly Correlated Physics" (NHSCP2014) at the Institute for Solid State Physics (ISSP), The University of Tokyo.

REFERENCE Physical Review B 89 (2014) 134422
DOI 10.1103/PhysRevB.89.134422
PREPRINT arXiv:1312.2643
AUTHOR Kouichi Okunishi and Kenji Harada
ABSTRACT Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, Kennedy-Tasaki's transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present temperature dependence of energy, entropy and string order parameter for the SO(N=3, 4, 5) BLBQ chains by the world-line Monte-Carlo simulation for the N-color bosonic particle model.

REFERENCE Physical Review Letters 112 (2014) 140603
DOI 10.1103/PhysRevLett.112.140603
PREPRINT arXiv:1307.0328
AUTHOR Akiko Masaki-Kato, Takafumi Suzuki, Kenji Harada, Synge Todo, Naoki Kaishima
ABSTRACT Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L\times L\times \beta t = 10240\times 10240\times 16$, using 3200 computing cores, which shows good parallelization efficiency.

３月２７日から３月３０日、

• 講演 "臨界現象に対する有意でない変数を考慮したベイズ流スケーリング解析手法" 27pAK-9
• 講演（共同研究者）"2次元 SU(N) J-Qモデルにおける脱閉じ込め転移と二つの長さスケール" 28pAK-14
• 講演（共同研究者）"正方格子、蜂の巣格子上一般化SU(N)Heisenberg模型の有限温度転移" 28pAK-15

From 3 March 2014 to 7 March 2014,

• Talk (Collaborator) "Parallelized Multi-Worm Algorithm for Large Scale Quantum Monte-Carlo simulations" C1.00284
• Talk (Collaborator) "Thermal phase transitions to valence-bond-solid states in the two dimensional SU(N) Heisenberg models" F7.00010
• Talk (Representative) "Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N" S27.00013

APS March Meeting 2014, Denver, Colorado, USA.

ツールキット BSAは臨界現象のスケーリング解析を行う新手法の参照コードです。ベイズ推定の力を用いて、自動的に臨界点や臨界指数を求めることができます。このツールキットBSAが、物質科学シミュレーションのポータルサイトMateriAppsにて紹介されました。

REFERENCE Physical Review B 88 (2013) 220408(R)
DOI 10.1103/PhysRevB.88.220408
PREPRINT arXiv:1307.0501v2
AUTHOR Kenji Harada, Takafumi Suzuki, Tsuyoshi Okubo, Haruhiko Matsuo, Jie Lou, Hiroshi Watanabe, Synge Todo, and Naoki Kaishima
ABSTRACT To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) N\'eel and valence-bond solid phases is characterized for $N=2,3,$ and $4$ on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y \equiv 1/\nu$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $\Psi^2$ for the SU(3) model.

１２月１０日から１２月１３日、 物性研スパコン共同利用・CMSI 合同研究会（第４回 CMSI 研究会）、東京大学物性研究所（柏キャンパス）。

PREPRINT arXiv:1312.2643
AUTHOR Kouichi Okunishi and Kenji Harada
ABSTRACT Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic(BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign free in the context of quantum Monte-Carlo simulation. For the SO(3) case, moreover, Kennedy-Tasaki's transformation for the S=1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present temperature dependence of energy, entropy and string order parameter for the SO(N=3, 4, 5) BLBQ chains by the world-line Monte-Carlo simulation for the N-color bosonic particle model.

From 2 Dec. 2013 to 5 Dec. 2013, Taipei Tensor Network Workshop 2013 , National Taiwan University, Taipei, Taiwan.

From 21 Oct. 2013 to 22 Oct. 2013,
CMSI International Symposium 2013: "Extending the power of computational materials sciences with K-computer" , Ito International Research Center in the University of Tokyo, Hongo Campus in Tokyo, Japan.

From 16 Oct. 2013 to 18 Oct. 2013, Satellite Meeting 2013 in Kobe: "CMSI Kobe International Workshop 2013: Recent Progress in Tensor Network Algorithms" , RIKEN Advanced Institute for Computational Science, Kobe, Japan.

９月２５日から９月２８日、

• 講演 "2次元 SU(N) J-Qモデルを用いた脱閉じ込め臨界現象の数値的研究" 25aKH-10
• 講演（共同研究者） "ワーム更新による並列化量子モンテカルロアルゴリズム" 25aKH-4
• 講演（共同研究者） "量子モンテカルロ法による正方格子SU(N)スピン模型の基底状態解析" 25aKH-8
• 講演（共同研究者） "シャストリーサザランド格子S=1/2反強磁性ハイゼンベルク模型の磁気秩序" 26pKM-1

８月１２日から８月１６日、"CMSI 第１部会「新物質・新量子相の基礎科学」 夏の学校 2013"、山形蔵王。

date: 2013-08-06 lang: all category: News, Conf

From 5 Aug. 2013 to 9 Aug. 2013, the International Conference on Strongly Correlated Electron Systems (SCES2013), University of Tokyo, Tokyo.

From 28 July 2013 to 31 July 2013, "Statistical Physics of Quantum Matter", National Taiwan University, Taipei, Taiwan.

PREPRINT arXiv:1307.0328
AUTHOR Akiko Masaki-Kato, Takafumi Suzuki, Kenji Harada, Synge Todo, Naoki Kaishima
ABSTRACT Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L \times L \times \beta t =10240 \times 10240 \times 16$, using 3200 computing cores, which shows good parallelization efficiency.

date: 2013-05-13 lang: all category: News, Talk

13 May 2013, the seminar of theory of electrons in solids group, Deptertment of Physics, Osaka University, Osaka.

３月２６日から３月２９日、

• 講演 "脱閉じ込め臨界現象の普遍性" 29aXZD-8
• 講演（共同研究者） "正方格子SU(N)スピン模型の有限温度転移" 29aXZD-9
• 講演（共同研究者） "ワームアルゴリズムの並列化" 29aXZD-11

From 18 March 2013 to 22 March 2013, APS March Meeting 2013, Baltimore, Maryland, USA.

PREPRINT arXiv:1212.1999
AUTHOR Jie Lou, Takafumi Suzuki, Kenji Harada, and Naoki Kaishima
ABSTRACT We performed variational calculation based on the multi-scale entanglemnt renormalization ansatz, for the antiferromagnetic Heisenberg model on a Shastry Sutherland lattice (SSL). Our results show that at coupling ratio J'/J= 0.687(3), the system undergoes a quantum phase transition from the orthogonal dimer order to the plaquette valence bond solid phase, which then transits into the antiferromagnetic order above J'/J=0.75. In the presence of an external magnetic field, our calculations show clear evidences of various magnetic plateaux in systems with different coupling ratios range from 0.5 to 0.69. Our calculations are not limited to the small coupling ratio region, and we are able to show strong evidence of the presence of several supersolid phases, including ones above 1/2 and 1/3 plateaux. Such supersolid phases, which feature the coexistence of compressible superfluidity and crystalline long range order in triplet excitations, emerge at relatively large coupling ratio (J'/J>0.5). A schematic phase diagram of the SSL model in the presence of magnetic field is provided.

１２月３日から１２月５日、 第３回 CMSI 研究会 〜超並列計算が拓く新しい計算物質科学〜、自然科学研究機構 岡崎コンファレンスセンター。

REFERENCE Physical Review B 86 (2012) 184421
DOI 10.1103/PhysRevB.86.184421
PREPRINT arXiv:1208.4306
ABSTRACT The ground state of an $S=1/2$ antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We apply a numerical variational method by using a tensor network with entanglement renormalization, which improves the capability of describing a quantum state. Magnetic ground states are identified for 0.7 <= J2 / J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the innerchain and interchain coupling constants, respectively. Except for the isotropic case (J1 = J2), the magnetic structure is spiral with an incommensurate wave vector that is different from the classical one. The quantum fluctuation weakens the effective coupling between chains, but the magnetic order remains in the thermodynamic limit. In addition, the incommensurate wave number is in good agreement with that of the series expansion method.