一维XY自旋链中双自旋比特的相干分布及其相变临界行为

Distribution of Two-spin Coherence and Their Critical Behavior in One-Dimensional XY Spin Chain

本文在具有Dzyaloshinsky-Moriya(DM)相互作用的一维XY自旋链中,以双自旋比特系统为研究对象,基于Jensen-Shannon熵,研究了量子相干分布(局域相干和集体相干)及其相变临界行为。研究发现,通过改变自旋-自旋耦合作用和DM相互作用,可以有效调控局域相干与集体相干之间的相互转化。此外,局域相干和集体相干能够通过局部极值或发散的临界行为准确地表征自旋链的一阶和二阶量子相变。当一阶量子相变的探测受到自旋-自旋耦合作用和DM相互作用的干扰时,集体相干比局域相干具有更加稳定的识别效果。最后,长距离自旋对的总体相干和集体相干在表征二阶量子相变上都具有显著优势。

Quantum coherence is one of the significant properties of quantum systems, and it is widely used in the quantum information processing and condensed matter physics. An important research topic is the correlation between the quantum coherence and the quantum phase transitions in the many-body system. However, most of the previous works mainly focused on the total coherence of quantum system, and the detection of quantum phase transitions can be hindered by some physical effects. It is well known that the total coherence and its distribution are closely related but also have their own unique properties. In order to overcome the failure of the detection, it is necessary to investigate the ability of coherence distribution to detect the quantum phase transitions and the impact of some physical effects on the detection. Moreover, how to regulate and control the coherence decomposition of a quantum system is very important for performing quantum information processing tasks. Whereas, the current researches cannot give a satisfactory answer.In this work, it is chosen as the research object that two-spin system surrounded by a one-dimensional XY spin chain with a Dzyaloshinsky-Moriya(DM) interaction. Based on Jensen-Shannon entropy, the coherence distributions(localized coherence and collective coherence) and their critical behaviors are investigated. By changing spin-spin coupling and DM interaction, the control of quantum coherence components in a two-spin system has been achieved. The strong spin-spin interaction increases the collective coherence of the two-spin system and reduces its localized coherence. The strong DM interaction increases localized coherence and reduces collective coherence. In addition, the localized coherence and collective coherence of the two-spin system can accurately characterize the first-order quantum phase transition through local extremums, but the spin-spin interaction and DM interaction seriously limit the accuracy of localized coherence in characterizing it. The first derivative of local coherence and collective coherence can accurately characterize the second-order quantum phase transitions through divergent behaviors, and is not affected by spin-spin coupling and DM interaction. Finally, it is found that the total coherence and collective coherence of long-distance spin pairs can accurately characterize first-order and second-order quantum phase transition through their critical behaviors. Especially for second-order quantum phase transition environments, the longer the lattice distance between spins, the more significant the critical behavior of the two types of coherence.