张量重正化群及其对量子自旋液体问题的研究

Recently there is a surge of interest on the investigation of quantum spin liquid in strongly correlated systems. Quantum spin liquid is a kind of topological state that does not show any spontoneous symmetry breaking. A thorough understanding of this novel quantum state is believed to be the key to the understanding of the pairing mechanism of high temperature superconductivity and related problems, in particular to the understanding of the origin of Mott insulators. We have worked on theory of strongly correlated electrons and on the density-matrix and tensor renormalization group methods for many years. This proposed project is to further develop and improve the tensor renormalization group method we have explored in recent years, and use it to study the ground state properties of the antiferromagnetic Heisenberg model on the Kagome lattice.We hope this to provide reliable numerical data that can help experimentalists to find undisputably quantum spin liquid state in frustrated quantum magentic materials. First, we will extend the global optimalization approach of second renormalization group to the double layer tensor network states to develope a novel tensor renormalization group method for accurately evaluating this kind of states. This method can be used not just for the study of this project, but also for the study of other problems of strongly correlated systems. Second, we will use this method, in combine with the tensor-network wave function of the so-called projected entangled simplex state recently proposed by group method, to calculate accurately the correlation functions and the entangment entropy for the antiferromagnetic Heisenberg model on the Kagome lattice, and from which to identify whether this ground state of this system is a quantum spin liquid.

量子自旋液体是一种新的拓扑量子态，这种量子态没有对称性的自发破缺，是强关联物理研究近年来的一个热点问题，是研究和解决高温超导及其相关的物理问题，特别是莫特绝缘体产生的机理问题的基础。申请人长期从事强关联量子理论及密度矩阵和张量重正化群方法的研究,本项目旨在这些工作的基础上，进一步发展和完善张量重正化群方法，并应用其研究Kagome晶格上反铁磁海森堡模型的基态性质，为实验上寻找量子自旋液体材料提供理论依据。主要研究的内容和目标，一是要运用全局优化的二次重正化群方法，建立精确计算双层张量网络态的重正化群方法，这种方法不仅对这个项目的研究有用，而且也可用于其它强关联量子问题的研究；二是运用这种方法，结合我们最近提出的投影纠缠单形态的波函数表示，精确计算Kogome海森堡模型的关联函数和纠缠熵，在此基础上对这个系统是不是一个量子自旋液体做出准确判断。

量子自旋液体是一种即使在零温下也不会发生对称性自发破缺的量子态，对这个问题认识对解决高温超导机理及其它强关联量子问题具有重要的意义。这个领域是凝聚态物理研究的一个前沿方向。在这个领域一个要解决的基本问题是，二维Kagome格子上的反铁磁海森堡相互作用的系统的基态是不是量子自旋液体，如果是，是有能隙还是无能隙的量子自旋液体。为了解决这个问题，我们通过这个项目，提出了一种新的收缩双层张量网络态的方法，大幅提高了张量重正化群的计算能力，并在此基础上，通过大规模数值计算，证明Kagome格子反铁磁海森堡模型的基态是一个无能隙的量子自旋液体，随后得到其他数值计算结果的支持，解决了这个长期争论的问题。