标题： 双层Kitaev-Heisenberg模型的量子相图 显示英文标题

标题： Quantum Phase Diagram of the Bilayer Kitaev-Heisenberg Model

摘要： 我们研究了基于无限投影纠缠对态技术的大规模张量网络计算的双层蜂窝晶格自旋-$1/2$Kitaev-Heisenberg模型的基态相图，以及高阶级数展开。 我们发现，在各种磁性有序相（包括铁磁、锯齿形、反铁磁（AFM）和条纹态）之外，在Kitaev极限附近出现了两个扩展的量子自旋液体相。 虽然这些有序相也出现在单层Kitaev-Heisenberg模型中，但我们的结果进一步表明，在AFM和条纹相之间的相对狭窄的参数空间范围内出现了一个价键固体态，该态可以绝热地连接到孤立的Heisenberg二聚体。 我们的结果强调了在双层Kitaev材料中出现新量子相时考虑层间相互作用的重要性。 显示英文摘要

摘要： We study the ground-state phase diagram of the spin-$1/2$ Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.