主讲人：刘文渊 研究员（浙江大学）

题目：Tensor Network Variational Monte Carlo Approach for 2D Quantum Many-body System: Algorithms and Applications（二维量子多体系统的张量网络变分蒙卡方法：算法和应用）

时间：2025年3月13日（周四）上午10：00

地 点：理工楼1226

联系人：罗洪刚

报告摘要：

Tensor networks, grounded in quantum entanglement, have emerged as a fundamental theoretical and numerical framework for studying strongly correlated systems. Matrix product states (MPS) serving as the variational space of the celebrated density matrix renormalization group (DMRG) method, have been the most powerful approach for 1D and quasi-1D quantum many-body problems. Their natural extension to higher dimensions, projected entangled pair states (PEPS), offers great potential for resolving challenging two-dimensional quantum systems. However, the computational complexity of PEPS has historically limited the development of practical and precise implementation methods.

以量子纠缠为基础的张量网络态，提供了描述强关联多粒子纠缠系统的理论框架和数值计算方法。其中，密度矩阵重正化群方法和其内蕴的矩阵乘积态(matrix product state)，已成为求解一维和准一维体系最为精确的方法， 并被广泛用于凝聚态物理和量子化学等。作为矩阵乘积态的高维推广，投影纠缠对态(projected entangled-pair state, PEPS)，为攻克二维量子多体难题提供了广阔的前景。然而，投影纠缠对态内在的复杂性，长期制约着其算法的发展，使得其实际潜力难以充分发挥。发展高效、精确的计算方法是张量网络领域的核心课题。

In this talk, I will introduce a PEPS approach through combining variational Monte Carlo. I will show that this method achieveshighaccuracy across multiple challenging systems: frustrated spin models, the Fermi-Hubbard model, and (2+1)D lattice gauge theories, thus establishing itself as a powerful tool for solving longstanding quantum many-body problems. Furthermore, I will present a new perspective on tensor networks----tensor network function, which expands the application of tensor networks into new directions and bridges the gap between pure neural networks and tensor networks.

本报告将介绍一种结合变分蒙卡和投影纠缠对态的二维张量网络计算途径。我们的研究表明，该方法在阻挫磁性体系、费米子哈伯德模型以及（2+1）维格点规范理论等多种极具挑战性的量子多体系统中，均可达到很高精度，这为解决诸多二维量子多体问题提供了新工具。此外，我将介绍“张量网络函数”这一新视角——它扩展了张量网络的应用领域，也在张量网络和神经网络之间架起了桥梁。

References:

(1)Wen-Yuan Liu et al, PRB 95, 195154 (2017)

(2)Wen-Yuan Liu et al, PRB 103, 235155 (2021)

(3)Wen-Yuan Liu et al, Sci. Bull. 67, 1034 (2022)

(4)Wen-Yuan Liu et al, PRX 12, 031039 (2022)

(5)Wen-Yuan Liu et al, Sci. Bull. 69, 190 (2024)

(6)Wen-Yuan Liu et al, PRL 133, 026502 (2024)

(7)Wen-Yuan Liu et al, PRB 109, 235116 (2024)

(8)Wen-Yuan Liu et al, PRL 133, 026502 (2024)

(9)Wen-Yuan Liu et al, arXiv:2502.13454 (2025)

(10) Yantao Wu, Wen-Yuan Liu, to appear soon. “Accurate Gauge-Invariant Tensor Network Simulations for (2+1)D Abelian Lattice Gauge Theory”

个人简介：

刘文渊，浙江大学百人计划研究员，博士生导师。2012年四川大学本科毕业，2017年中国科学技术大学博士毕业，之后在香港中文大学、香港大学和加州理工学院从事博士后研究，2024年10月加入浙江大学物理高等研究院。长期从事张量网络等量子多体计算方法的发展，研究兴趣包括量子阻挫磁性，强关联电子体系，格点规范场论，量子模拟，机器学习等。