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Fermionic path integrals and correlation dynamics in a 1D XY system
Annals of Physics ( IF 3 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.aop.2020.168286
I. Lyris , P. Lykourgias , A.I. Karanikas

We derive time dependent correlation functions in an one dimensional XY spin model with the use of generating functionals, the latter being defined as path integrals over fermionic coherent states. We focus on the proper construction of the aforementioned integrals in order to avoid the inconsistencies accompanying the corresponding functional integrals over spin coherent states and we prove that, at the static limit, the known results are reproduced. In the same context, we examine the case of a driven transverse magnetic field and we confirm the consistency of our results with the Kibble-Zurek mechanism.

中文翻译:

一维 XY 系统中的费米子路径积分和相关动力学

我们使用生成函数在一个一维 XY 自旋模型中推导出时间相关函数,后者被定义为费米子相干态上的路径积分。我们专注于上述积分的正确构造,以避免伴随自旋相干状态的相应功能积分的不一致,并且我们证明,在静态极限下,已知结果被再现。在相同的背景下,我们检查了驱动横向磁场的情况,并确认了我们的结果与 Kibble-Zurek 机制的一致性。
更新日期:2020-10-01
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