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.

• Received 29 October 2019
• Revised 31 January 2020
• Accepted 10 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115142