We investigate quantum-phase transitions (QPT) in the Ising transverse field model, the XY-Heisenberg model with staggered Dzyaloshinskii–Moriya (DM) interaction, and the bond alternating Ising model with DM interaction, on a one-dimensional periodic chain using the quantum renormalization group (QRG) method. Based on \({l_1}\)-norm and relative entropy, we employ two quantum coherence measures to identify QPT. Our results show that the QPT can be characterized by the coherence measure calculated for each QRG step. It is found that after large number of QRG iterations, the coherence in the ground state develops two saturated values corresponding to two different phases and changes abruptly at a quantum critical point (QCP). The scaling behavior of the system is investigated by computing the derivative of the coherence measure around the QCP that shows a logarithmic dependence on the length of the chain. The critical exponent of the correlation length is also calculated.

中文翻译：

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$$ {l_1} $$ l1-范数的量子重归一化和量子自旋链中相干性的相对熵

我们使用一维周期链，在Ising横向场模型，具有交错的Dzyaloshinskii-Moriya（DM）相互作用的XY-Heisenberg模型以及具有DM相互作用的键交替Ising模型中研究量子相变（QPT）。量子重归一化组（QRG）方法。基于\（{l_1} \）-范数和相对熵，我们采用两种量子相干度量来识别QPT。我们的结果表明，QPT可以通过为每个QRG步骤计算的相干度量来表征。发现在大量QRG迭代之后，基态的相干性产生了对应于两个不同相位的两个饱和值，并在量子临界点（QCP）突然改变。通过计算QCP周围的相干度量的导数来研究系统的缩放行为，该导数显示了对链长度的对数依赖性。还计算了相关长度的临界指数。