一个问题：具有Dzyaloshinskiii-Moriya相互作用的XY自旋链系统中的量子临界现象
A Question: Quantum Critical Phenomena in XY Spin-Chain Systems With Dzyaloshinskii-Moriya Interactions
摘要：
Jordan-Wigner变换和Bogolyubov变换是哈密顿量对角化的主要步骤，在一维海森堡自旋链模型的统计力学计算中起着重要作用。有许多方法可以用来探测量子相变、临界区和相变附近的标度行为，如几何相位、保真度磁化率、序参量和纠缠熵等，它们都与Bogolyubov变换有直接的关系。对具有Dzyaloshinskiii-Moriya相互作用的XY自旋链系统的哈密顿量进行对角化，结果表明，只有能谱而不是Bogolyubov变换系数依赖于DM相互作用.因此，DM相互作用可能不会影响量子相变的临界磁场，也不会在XY自旋模型中引入新的临界区。在此基础上，进一步利用几何相的方法证明了这一观点。
英文摘要：
Jordan-Wigner transformation and Bogolyubov transformation are the main steps of the diagonalization of Hamiltonian and paly an important role in the statistical mechanics calculations for one-dimensional Heisenberg spin chain model. Many methods can be exploited as a tool to detect quantum phase transition, regions of criticality and scaling behavior in the vicinity of a quantum phase transition, such as geometric phase, fidelity susceptibility, order parameter, and entanglement entropy, which have direct relation with Bogolyubov transformation. We diagonalized the Hamiltonian in XY spin-chain systems with Dzyaloshinskii-Moriya interactions, the results shows that only the energy spectrum but not the coefficients of the Bogolyubov transformation depends on DM interaction. Therefore, the DM interaction may not influence the critical magnetic field of quantum phase transitions and not induce new critical regions in the XY spin model. Moreover, we further prove the ideas by the methods of geometric phases in this model.
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