二维自旋系统中退禁闭量子临界行为的数值研究

退禁闭量子相变是发生在两个破缺不同对称性有序相之间的连续相变，伴随相变点涌现对称性和退禁闭自由度出现，是一类不符合朗道相变理论的新奇相变类型。其中一个例子是自旋系统中反铁磁态到价键固体态之间的连续相变，目前理论上关于此类相变在热力学极限下的连续性以及涌现对称性的存在与否仍有很大争议。本项目对易面J-Q模型上反铁磁态到价键固体态的相变进行量子蒙特卡洛数值计算分析，得到易面J-Q模型不同各向异性强度与序参量临界值的关系，并进一步分析该模型上热力学极限下出现退禁闭量子相变的各向异性强度参数范围，为判断J-Q模型在热力学极限下是否真实连续提供一个全新的思路和证明。同时通过序参量的分布统计和系统守恒流分析，给出易面J-Q模型在各项异性强度较小时系统发生一级相变但共存区有涌现对称性的直接证据。此外，运用随机解析延拓方法给出系统不同情况下的自旋激发谱图，吸引实验对退禁闭量子临界现象的广泛关注。

Deconfined quantum critical point describes an exotic continuous phase transition happens between two ordered phases that break completely different symmetries with an emergent symmetry and a deconfined degree of freedom at the critical point, which should be a first-order transition according to the widely accepted Landau phase transition theory. One of the most important examples in deconfined quantum phase transition is the continuous phase transition between Neel state and the valence bond solid (VBS) state in spin systems. There are lots of related theoretical and computational studies in this transition in recent few years. However, it is still not quite clear whether the transition between Neel and VBS is continuous and if there is an emergent symmetry at the critical point. .In order to find ways to answer those questions we study a series of easy-plane J-Q model where a Neel to VBS phase transition would happen using quantum Monte Carlo simulation method in this project. We can get the relation between converged values of two order parameters at critical point and the strength of anisotropy from our simulation. The range of the anisotropic strength value where a continuous phase transition happens could be got afterwards, which provides a new viewpoint to prove the continuity of the phase transition in previous normal isotropic J-Q model. Besides, we will also study the distribution of order parameters and the conserved currents in the system to test the symmetry in easy-plan J-Q models at certain anisotropic strength in order to find unconventional examples with discontinuous transition and emergent symmetry simultaneously. In the end we will study the dynamic spin structures in different phases using stochastic analytical continuation method and show the spin excitation spectrums which could be directly measured in experiment to attract more interest in experimental study on deconfined quantum criticality.