张量网络算法的环路优化及其对二维强关联电子系统的研究

The recently developed tensor network methods can overcome the limitations of various traditional methods, thus shed new light on solving strongly correlated problems. However, the efficiency and accuracy of the two dimensional tensor network wave functions are yet to be improved. Our early work shows a loop optimization step is helpful for dealing with critical systems or systems with long-range entanglement. In this project, we will develop a series of new tensor network algorithms based on loop optimization, which serve as accurate approaches for studying the ground state properties of two-dimensional strongly correlated electron models. We will calculate the charge densities and order parameters of Hubbard model and t-J model on a square lattice with different dopings. These will help us to identify the possible spin, charge, and Cooper pair orders, as well as their relations with the superconducting phase and the pseudo-gap phase. We will further consider the effects of the next-nearest neighbor hopping terms. Our study will provide solid evidences for revealing the mechanism of superconducting pairing in high temperature superconductors.

近年来新兴的张量网络计算方法可以克服传统手段的各种局限性，为解决强关联量子多体问题带来新的希望。但是对于二维张量网络变分波函数的求解，计算效率和精度还需要进一步的提高。我们的前期工作发现，环路优化步骤可以更有效的处理临界系统和具有长程纠缠的系统。本项目拟发展一系列基于环路优化的新型张量网络方法，并用它们来精确研究二维强关联电子模型的基态性质。我们将计算方晶格Hubbard模型和t-J模型在不同掺杂情况下的电荷密度和配对序参量，识别出可能存在的自旋有序态、电荷有序态、配对密度波等新奇有序态，并展示它们与超导态和赝能隙态的关联。我们还将进一步考虑次近邻跃迁对d波配对的影响。本项目将为揭示高温超导电子配对的微观机理提供可靠的科学依据。

张量网络态可以描述量子多体系统内部的纠缠特性，近年来逐渐发展成研究量子多体物理的有效数值方法之一。本项目发展了新型的带有环路优化步骤的二维张量网络算法，减少了虚时演化中的截断误差，对临界系统可以得到更精确的临界点和临界指数。我们基于二维费米子投影纠缠对态，编写和完善了一系列费米子张量网络程序，在热力学极限下研究了蜂窝晶格和方晶格上t-J模型及Hubbard模型的基态和关联函数，计算了系统基态能量、电荷密度、局域磁化、配对序参量等物理量。此外，我们还利用张量网络方法，研究了无能隙拓扑畴壁的临界性质、耗散量子多体系统中的动力学对称性、里德堡原子系统中的量子输运、多体量子态的拓扑序探测等方面。