We review the internal connection between quantum coherence (QC) and quantum phase transitions (QPTs). We propose two quantities $L_{\text{QC}}$ and $S_{\text{QC}}$ to detect QPTs of different orders by analyzing the spectrum of QC. Our results show that the two quantities not only can detect different types of QPT but can also exhibit a remarkable robustness against thermal fluctuations. In comparison with other detectors, such as quantum entanglement and QD, $L_{\text{QC}}$ and $S_{\text{QC}}$ can show more effective and reliable behaviors in characterizing a QPT at zero and finite temperatures. In light of this property and the fundamental role of QC in quantum information processing, QC spectrum-related $L_{\text{QC}}$ and $S_{\text{QC}}$ have considerable importance in detecting QPTs at a real finite-temperature experimental environment.

中文翻译：

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量子相干谱和量子相变

我们回顾了量子相干性（QC）和量子相变（QPT）之间的内部联系。我们建议两个数量${\mathrm{大号}}_{\text{质量控制}}$ 和 ${\mathrm{小号}}_{\text{质量控制}}$通过分析QC的频谱来检测不同阶次的QPT。我们的结果表明，这两个量不仅可以检测不同类型的QPT，而且还可以表现出显着的抗热波动性。与其他探测器（例如量子纠缠和QD）相比，${\mathrm{大号}}_{\text{质量控制}}$ 和 ${\mathrm{小号}}_{\text{质量控制}}$可以在零和有限温度下表征QPT时表现出更有效和可靠的行为。鉴于此特性以及QC在量子信息处理中的基本作用，QC频谱相关${\mathrm{大号}}_{\text{质量控制}}$ 和 ${\mathrm{小号}}_{\text{质量控制}}$ 在实际的有限温度实验环境中检测QPT至关重要。