Ghent University

Abstract: The contraction of tensor networks is a central task in the application of tensor network methods to the study of quantum and classical many body systems. In this paper, we investigate the impact of gauge degrees of freedom in the virtual indices of the tensor network on the contraction process, specifically focusing on boundary matrix product state methods for contracting two-dimensional tensor networks. We show that the gauge transformation can affect the entanglement structures of the eigenstates of the transfer matrix and change how the physical information is encoded in the eigenstates, which can influence the accuracy of the numerical simulation. We demonstrate this effect by looking at two different examples. First, we focus on the local gauge transformation, and analyze its effect by viewing it as an imaginary-time evolution governed by a diagonal Hamiltonian. As a specific example, we perform a numerical analysis in the classical Ising model on the square lattice. Second, we go beyond the scope of local gauge transformations and study the antiferromagnetic Ising model on the triangular lattice. The partition function of this model has two tensor network representations connected by a non-local gauge transformation, resulting in distinct numerical performances in the boundary MPS calculation.

报告人简介：唐维，2016年于南京大学获得物理学学士学位，2021年于北京大学量子材料中心获得凝聚态博士学位。目前在比利时根特大学从事博士后研究工作。目前主要的研究领域为张量网络方法及其在量子多体物理问题中的应用。

Contact: Lei Wang 9853