Title: Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo Show Chinese title

Title: 扩展Kitaev蜂窝模型中的多节点量子自旋液体：变分蒙特卡洛的视角

Abstract: We discuss the discovery by variational Monte Carlo (VMC) methods of a series of multinode quantum spin liquids (QSLs) in extended Kitaev models on the honeycomb lattice. Like the gapless Kitaev spin liquid with its two nodes at K and K$^\prime$, these multinode QSLs are characterized by an emergent Z$_2$ gauge structure and a discrete number of symmetry-protected Majorana cones in their low-energy excitation spectrum. Because the cones are gapped by weak magnetic fields, nonzero Chern numbers are obtained and the ground state becomes one of many possible Abelian or non-Abelian chiral spin liquids. Here we focus on the projective symmetry group (PSG)-guided VMC approach to the Kitaev model with various symmetry-allowed extended interactions. Based on the VMC phase diagrams of these models, we propose a framework for the classification of nodal QSLs that includes the PSG, the chiralities of the cones, and the way in which the cones are symmetry-related. At present, the known candidate Kitaev materials seem to lie outside the parameter regimes of the multinode QSL phases. However, with more than 100 Z$_2$ PSGs for spin-orbit-coupled states on the honeycomb lattice, we anticipate that more than one multinode QSL will be realized experimentally in future work. Show Chinese abstract

Abstract: 我们讨论了通过变分蒙特卡洛（VMC）方法在蜂窝状晶格扩展的基塔耶夫模型中发现的一系列多节点量子自旋液体（QSL）。与具有K和K$^\prime$两点的无隙基塔耶夫自旋液体类似，这些多节点QSL由一个新兴的Z$_2$规范结构以及低能激发谱中的离散数量的对称保护马约拉纳锥所表征。由于锥体被弱磁场打开间隙，因此得到了非零的陈数，基态成为许多可能的阿贝尔或非阿贝尔手征自旋液体之一。在此，我们专注于投影对称群（PSG）引导的VMC方法来处理具有各种对称允许扩展相互作用的基塔耶夫模型。基于这些模型的VMC相图，我们提出了一种用于分类节点QSL的框架，其中包括PSG、锥体的手征性以及锥体之间的对称关系。目前，已知的候选基塔耶夫材料似乎位于多节点QSL相的参数范围之外。然而，在蜂窝状晶格自旋轨道耦合状态下有超过100个Z$_2$PSG，我们预计在未来的工作中将实现不止一种多节点QSL。