In this paper, we have used the state finder hierarchy for Barrow holographic dark energy (BHDE) model in the system of the FLRW Universe. We apply two DE diagnostic tools to determine $\Lambda BHDE$ model to have various estimations of $▵$. The first diagnostic tool is the state finder hierarchy in which we have studied $S_3^{\left(1\right)}$ $S_4^{\left(1\right)}$, $S_3^{\left(2\right)}$ $S_4^{\left(2\right)}$ and second is the composite null diagnostic (CND) in which the trajectories ($S_3^{\left(1\right)}-ϵ$), ($S_4^{\left(1\right)}-ϵ$), ($S_3^{\left(2\right)}-ϵ\left)\right(S_4^{\left(2\right)}-ϵ$) are discussed, where $ϵ$ is fractional growth parameter. The infrared cut-off here is taken from the Hubble horizon. Finally, together with the growth rate of matter perturbation, we plot the state finder hierarchy that determines a composite null diagnosis that can differentiate emerging dark energy from $\Lambda CDM$. In addition, the combination of the hierarchy of the state finder and the fractional growth parameter has been shown to be a useful tool for diagnosing BHDE, particularly for breaking the degeneracy with different parameter values of the model.

在本文中，我们在FLRW宇宙系统中将状态查找器层次结构用于Barrow全息暗能量（BHDE）模型。我们使用两种DE诊断工具来确定$\Lambda 乙HdE$ 模型具有各种估计 $▵$。第一个诊断工具是我们研究过的状态查找器层次结构${\mathrm{小号}}_3^{（\mathrm{1个}）}$ ${\mathrm{小号}}_4^{（\mathrm{1个}）}$， ${\mathrm{小号}}_3^{（\mathrm{2个}）}$ ${\mathrm{小号}}_4^{（\mathrm{2个}）}$ 第二个是复合空诊断（CND），其中轨迹（${\mathrm{小号}}_3^{（\mathrm{1个}）}-ϵ$），（${\mathrm{小号}}_4^{（\mathrm{1个}）}-ϵ$），（${\mathrm{小号}}_3^{（\mathrm{2个}）}-ϵ）（{\mathrm{小号}}_4^{（\mathrm{2个}）}-ϵ$），其中 $ϵ$是分数增长参数。此处的红外截止是从哈勃望远镜的地平线上截取的。最后，连同物质扰动的增长率，我们绘制了状态查找器层次结构，该层次结构确定了可以将新兴暗能量与$\Lambda Cd\mathrm{中号}$。此外，状态发现器的层次结构和分数增长参数的组合已被证明是诊断BHDE的有用工具，特别是对于打破模型不同参数值的简并性而言。