Topology and Entanglement in Quantum Many-Body Systems

I. Coordinator:
  • Prof. Pochung Chen (NTHU).

II. Core Members:

  • Core members
  • Profs. Ying-Jer Kao (NTU), Prof. Yu-Cheng Lin (NCCU), Prof. Hong-Yi Chen (NTNU), Prof. Ming-Chiang Chung (NCHU), Prof. Po-Yao Chang (NTHU).
  • Postdocs
  • Dr. Ching-Yu Huang (NCTS), Dr. Adam Laizzi (NTU), Dr. Yao-Tai Kang (NTHU)
  • Students
  • Kai-Hsin Wu (PhD). Adam Iaizzi (post D), Chih-Yuan Lee (PhD), Wen-Han Kao (PhD), Kai-Hsin Wu (PhD), Jing-Jer Yan, Jui-Hui Chung, Ting-Kai Kuo, Cheng-Wei He, Taiyi Zhang, Chung-Yu Lo(PhD), Yuan-Chun Lu, Zheng-Lin Tsai.

III. Research Themes:

  • Entanglement structure in interacting topological and disordered systems
  • Many interesting physics problems in strongly correlated systems are difficult to solve, and require non-perturbative methods as AdS/CFT duality or Matrix/Tensor product states to tackle. Quantum entanglement has recently been regarded as a bridge between these seemingly different viewpoints, and it may hold the key to understand some exotic phases in these systems.
  • We propose to study these subjects:
  • • Wavelet transformation and topological order.
    • Entanglement structures in disordered system with strong interaction.
    • Entanglement structures in many-body localization.
  • Topology and entanglement in non-equilibrium systems
  • Non-equilibrium many-body quantum systems are challenging and interesting. To further develop the concept of non-equilibrium phases of matter, new theoretical 
    and numerical tools are required. We aim to develop necessary tools that can be used to investigate the topology and entanglement in non-equilibrium systems.
  • We propose to study these subjects:
  • • Topology and entanglement in quench and driven dynamics.
    • Entanglement in non-equilibrium CFT.
    • Integrable methods on non-equilibrium phases.
  • Machine learning and Physics
  •    In the past years, significant progresses have been made in machine learning algorithms that have been used in the classification and interpretation of large data sets, sparking a revolution in areas such as image and natural language processing.
  •    Recently, it has been understood that the fundamental concepts behind the success of machine learning is closely related to the renormalization group in statistical physics. This raises the important question of what further insights remain to be found at the intersection of machine learning and fields such as statistical physics, condensed matter, and quantum information.
  • We propose to explore these research directions:
  • • Use techniques from machine learning to tackle quantum many-body problems.
    • Explore the possible connections between deep learning, the renormalization group, and tensor networks/MERA.
    • Application of reinforcement learning in quantum control and error corrections.


IV. Activities:

  • We plan to organize the following academic activities:
  • •  (9/2019) Workshop on Topology & Entanglement in Non-Equilibrium Systems
  • Non-equilibrium many-body quantum systems are challenging and interesting.They sit at the interface between condensed matter physics, quantum information,
    high-energy physics, and computational physics. To further develop the concept of non-equilibrium phases of matter, however, new theoretical and numerical tools are required to describe the dynamics of quantum systems far-from equilibrium. This workshop focuses on recent developments on the dynamics of quantum entanglement and topology in non-equilibrium systems. We will gather leading theoretical and experimental experts on various topics of non-equilibrium quantum systems, including quench dynamics, driven systems, tensor networks, and quantum integrability. This will lead to extensively discussing and novel developments of interdisciplinary methods of understanding non-equilibrium quantum systems 
  • •  (12/2019) Workshop on Tensor Network States: Algorithms and Applications
    In this workshop, we will bring together experts on tensor network state algorithms, and their wide spectrum of applications. We will also devote time in the workshop to explore the application of machine learning techniques to statistical physics, and the relation with the tensor network states. Research talks will be complemented with pedagogical lectures and tutorials. 
  • •  (4/2020) Workshop on Machine Learning and Physics
    In this workshop we invite experts in the emerging research area that applies machine learning techniques to analyze, represent, and solve quantum many-body systems in condensed matter physics. The subjects include problems of phase classification and characterization, state compression, feature extraction, neural networks as representation of wavefunction, interplay between tensor networks and machine learning, and applications in quantum control and quantum error correction.
  • •  (9/2020) Summer School
  • We plan to hold a one-week summer school designed to train young scientists (students and postdocs) to familiarize them with necessary techniques. We will build on past successful experience and continue to offer high quality lectures and hands-on tutorials. The summer school also serves as a platform for students from different universities to interact with each other.
  • •  Hackathon
  • We plan to hold 1day hackathon once per semester. The idea is to bring all members together and solve some technical issues together and to train members to learn essential technique for the related research. It also provides an opportunity to brainstorm new ideas and forge new collaborations.
  • •  Internatinal visitors
  • We will continue to invite international visitors to further current/forge new collaborations. We expect each visitor to stay at least a week to interact intensively
    with the members.


. Expected achievements:

  • 1. Strengthening collaboration among core members.
  • 2. Training for junior scientists.
  • 3. Strengthening and expanding our international collaboration.
  • 4. World leading research.
  • 5. Exploring the interdisciplinary research among condensed matter physics, string theory, quantum information science, and computer science.


. Collaborations:

  • Current international collaborations
  • Currently, we are collaborating with the following international researchers. With the support from the thematic group, we plan to have mutual visits to further the collaborations.
  • • Prof. Anders Sandvik (Boston University, USA)
  • • Prof. Tzu-Chieh Wei (SUNY Stony Brook, USA)
  • • Prof. Roman Orus (Johannes Gutenberg-Universität, Mainz, Germany)
  • • Prof. Frank Pollmann (Technische Universität München, Germany)
  • • Prof. Andreas Läuchli (Universität Innsbruck, Austria)
  • • Dr. Ian McCullouch (University of Queensland, Australia)
  • • Prof. Masaki Oshikawa (ISSP, University of Tokyo, Japan)
  • • Prof. Xin Wan (Zhejiang University, China)
  • • Prof. Bill Atkinson (Trent University, Canada)
  • Potential new international collaborations
  • We plan to invite following international researchers to foster future collaborations.
  • • Prof. Garnet Chan (Princeton, USA)
  • • Prof. Yang Qi (IAS of Tsing-Hua University, China)
  • • Prof. Rachel Wortis (Trent University, Canada)
  • • Prof. Malcolm Kennett (Simon Fraser University, Canada)
  • • Prof. Ling Wang (Computational science researcher center, China)
  • • Prof. Z. Y. Xie (Renmin University, China)
  • • Prof. Lei Wang (Institute of Physics, CAS, China)
  • • Prof. Roger Melko (University of Waterloo/Perimeter Institute, Canada)
  • • Prof. Juan Carrasquilla (Vector Institute of Artificial Intelligence, Canada)
  • • Prof. Tarun Grover (University of California, San Diego, USA)
  • • Prof. Dong-Hee Kim (Gwangju Institute of Science and Technology, S. Korea)

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