Two-dimensional tensor-network study of real-time dynamics in quantum many-body systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K13855
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Waseda University (2023); Kindai University (2021-2022)
• Principal Investigator: Kaneko Ryui 早稲田大学, 理工学術院, 主任研究員 (10881211)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: テンソルネットワーク / 量子多体系 / 非平衡系 / 冷却原子系 / 量子シミュレータ / Rydberg原子 / 量子スピン系 / 時間発展

Outline of Final Research Achievements

In this study, we computed the real-time dynamics of two-dimensional quantum systems, which are challenging for conventional numerical methods, using the tensor network method based on the projected entangled pair state (PEPS). Focusing on the quench dynamics of quantum many-body systems achievable in experiments with ultracold atoms in optical lattices, we calculated the time and distance dependence of correlation functions in various systems, providing valuable reference data for future experiments. We also extensively investigated the interaction dependence of the group velocity of correlation propagation to examine the upper bounds of quantum information propagation speed, Lieb-Robinson bounds, whose exact values are unknown in quantum many-body systems for more than one spatial dimension in general.

Free Research Field

数理物理、物性基礎／磁性、超伝導、強相関系／半導体、光物性、原子物理

Academic Significance and Societal Importance of the Research Achievements

本研究の成果は、今後の光格子中の冷却原子気体や光ピンセット配列中のRydberg原子集団におけるダイナミクスの実験結果を理解する上で有用である。また、今回数値的に得られた相関伝播の群速度は、今後、厳密なLieb-Robinson限界を得る際の重要な足掛かりとなる。量子多体系の非平衡ダイナミクスを理解する上で、学術的意義が大きい。さらに、アナログ量子シミュレーションと相補的な、古典計算機上の数値シミュレーションの技術を高めることは、社会的に注目を集めている量子計算技術の進展にも役立つと期待される。