Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the $(2+1)$-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.

中文翻译：

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蜂窝晶格上里德堡原子的密度波有序相

里德堡原子阵列最近已成为探索物质的奇异量子相和量子现象的有前途的平台。在这项工作中，我们通过执行大规模有限尺寸密度矩阵重整化组模拟，绘制了蜂窝晶格上里德堡原子的基态相图作为里德堡封锁半径和激光失谐的函数。除了无特征的无序相外，我们还在相对宽的参数空间内发现了其他五个复杂的长程密度波有序相。通过计算它们的里德堡激发曲线和静态结构因子来分析这些量子相的特性。此外，一个连续的量子相变属于$(2+1)$维伊辛普适性类通过标准的有限尺寸缩放分析进行探索。我们的工作暗示了一些不同的物理学，例如可能的非平凡量子相变和高度简并的弦有序相，蜂窝几何可以为里德堡系统带来并作为可能的真实实验的数值指南。