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Tensor network states provide a powerful framework for simulating quantum manybody systems, offering insights into a variety of quantum phases, including topological orders, symmetry-protected topological (SPT) phases, and critical phenomena. While extensive research has been conducted on tensor networks for spin systems, such as matrix-product states (MPS) and projected entangled pair states (PEPS), the application of tensor networks to fermionic systems has garnered increasing interest more recently. In this presentation, I will delve into our recent advancements in the development and implementation of fermionic tensor networks. We introduce a novel construction based on Gaussian states in arbitraryspatial dimensions, and translate the Gaussian tensor networks into many-body Hilbert spaces. As a case study, I will highlight our computation of correlation functions in Gutzwiller projected Fermi sea states within one-dimensional systems, demonstrating the utility and precision of our approach.
References:
[1] Kangle Li, Yan-Bai Zhang, Hoi Chun Po, arXiv: 2408.00858
[2] Yuman He, Kangle Li, Yan-Bai Zhang, Hoi Chun Po, arXiv: 2308.09377
Kangle Li is in his fourth year as a PhD student at the Hong Kong University of Science and Technology (HKUST). He got his bachelor’s degree from University of Science and Technology of China in 2018. From 2021 Spring, he started his PhD program in HKUST, under the supervision of Prof. Hoi Chun Po. His research interests mainly lie on quantum many-body systems, including the tensor network methods in representing correlated many-body states. He is also interested in the interplay of quantum information and quantum many-body problems.
Tencent meeting link: https://meeting.tencent.com/dm/xOGm10IhlBm6 Meeting ID: 975 766 599, no password