We use multipartite entanglement and trace distance to detect the quantum phase transitions of the extended one-dimensional compass spin-chain model by applying the density matrix renormalization group method which is represented by the matrix product state. It is shown that singular behaviors of the first-order derivative of the multipartite entanglement and trace distance occur at the critical point of the system. The scaling behaviors of trace distance and multipartite entanglement are also discussed, and we show that the universal finite-size scaling law is valid for the multipartite entanglement and trace distance around the critical point. Moreover, we explore the quantum coherence for this model and find that the first-order derivative of the quantum coherence also displays discontinuity and exhibits singular critical behaviors that are the same as the trace distance and multipartite entanglement.

中文翻译：

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一维罗盘自旋链模型的量子相变和缩放行为

我们使用多方纠缠和迹线距离，通过应用以矩阵乘积状态表示的密度矩阵重新归一化群方法，来检测扩展的一维罗盘自旋链模型的量子相变。结果表明，多纠缠和跟踪距离的一阶导数的奇异行为发生在系统的临界点。还讨论了迹线距离和多部分纠缠的缩放行为，并且我们证明了通用有限尺寸缩放定律对于临界点附近的多部分纠缠和迹线距离是有效的。此外，