阻挫晶格体系中量子拓扑激发的理论研究

Researches on the topological phase transition and topological phase of matter are frontier topic in the condensed matter physics, especially in the strongly correlated systems. As an intrinsic critical role, the topological excitations are the key to understand the mechanism of the topological phase and topological phase transitions. Recently, by numerically simulating the two-dimensional frustrated system, we found the string type quantum topological excitation can induce the deconfined phase transition and many exotic quantum phases such as fractional edge liquid, incommensurate supersolid and spin liquid. In order to better understand the mechanism of the topological excitations, firstly in this project, by using exact diagonalization and effective field theory, we plan to find the form of the effective interactions between quantum strings. Secondly, we plan to study the effect of next-nearest neighbor interaction in the Kagome optical lattice with large scale quantum Monte Carlo simulation, and a possible incommensurate valence bond solid may emerge. At last, we plan to study the XXZ model in the anisotropic triangular lattice with two-dimensional density matrix renormalization group for searching the incommensurate coplanar phase and spin liquid. This project is not only aim to understand quantum topological excitation better and search for new exotic quantum topological phases, but also can help to understand the possible spin liquid in the quantum antiferromagnets with anisotropic triangular geometry.

拓扑物态及拓扑相变的研究一直以来都是凝聚态物理，特别是强关联体系中的前沿课题。而作为内部重要环节的量子拓扑激发，则成为理解量子拓扑态以及拓扑相变机制的关键因素。近几年来，我们通过对二维阻挫晶格系统数值模拟发现，弦类型的量子拓扑激发诱发了诸如分数核边缘态，非相称超固体和自旋液体等新奇量子相以及退禁闭量子拓扑相变。为了深入理解量子拓扑激发的性质和影响，本项目计划首先利用精确对角化计算量子弦间的有效相互作用形式；之后通过在Kagome晶格中引入次近邻相互作用，利用量子蒙特卡洛模拟找寻新的非相称共价键固体态，并得到全相图；最后，通过二维密度矩阵重整化群方法在各向异性三角晶格中找寻非相称共面态以及可能的自旋液体相。本项目不仅有助于加深对量子拓扑激发的认识理解，更有可能探寻到新奇量子拓扑态，同时对于各向异性三角晶格反铁磁材料中可能出现的自旋液体的理解也有着重要意义。

量子阻挫系统一直以来是凝聚态领域的重要课题。然而，由于量子多体系统的复杂性，解析方法非常有限。此项目中，我们开发了针对量子阻挫体系的大规模量子蒙特卡洛数值模拟程序，并将其应用于量子阻挫磁性系统和超冷原子光晶格体系的相关模型中。在三角晶格横场伊辛模型的动力学计算中，我们发现系统中存在自旋子和量子弦形式的拓扑激发，并利用随机解析延拓研究了其对应的动力学行为，提出了可能的量子弦拉廷恩液体相。另一方面，研究了光腔与二维光镊阵列内里德堡原子的耦合系统，发现不同于一维情况，两序共存的超辐射固体态的参数存在区间大幅增加。除此之外，与中科院国家授时中心的实验团队合作，我们研究了光晶格钟系统的弗洛凯问题。项目结题时共发表PRL、CPL、PRB等文章10篇，其中PRL三篇，npj Quantum material 一篇。