We detect the quantum phase transition of the ground state from the excited state by using the cluster density matrix embedding theory to calculate the excited state of the J₁ − J₂ model. By analyzing the excitation energy gap of the transformation in the system, we detect that the critical point of the intermediate phase of ground state is J₂ \( \simeq \) 0.5. With the increase of energy, the new valence bond solid (VBS) order appears in the excited state, which is different from that in the ground state.

中文翻译：

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通过激发态检测量子相变

我们通过使用簇密度矩阵嵌入理论来计算J ₁ − J ₂模型的激发态，从而检测基态从激发态的量子相变。通过分析系统中变换的激发能隙，我们检测到基态中间相的临界点是J ₂ \( \simeq \)0.5. 随着能量的增加，新的价键固体（VBS）有序出现在激发态，不同于基态。