Entanglement after quantum quenches in Lifshitz scalar theories
Entanglement after quantum quenches in Lifshitz scalar theories
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DOI：
10.1088/1742-5468/ab417f
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发表时间：
2019-06
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通讯作者：
Keun-Young Kim;M. Nishida;M. Nozaki;Minsik Seo;Yuji Sugimoto;A. Tomiya
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作者：
Keun-Young Kim;M. Nishida;M. Nozaki;Minsik Seo;Yuji Sugimoto;A. Tomiya
用关联方法研究了动力学指数为z>；1的Lifshitz自由标量理论中量子猝灭后纠缠熵的时间演化。对于量子猝灭，我们考虑了两种依赖于时间的质量函数：末端临界协议(ECP)和顺式临界协议(CCP)。在这两种情况下，早期的纠缠熵与子系统的大小无关。在一个临界时间(TC)之后，纠缠熵开始显著地依赖于子系统的大小。快速ECP和CCP中z=1的临界时间TC已被准粒子图像中的快速准粒子很好地解释。然而，我们发现，对于z>；1，这个解释不成立，TC被延迟。我们根据准粒子图像解释了TC延迟到z>；1的原因：本质上，这是由于快和慢准粒子之间的竞争。在后期，在ECP中，纠缠熵缓慢增加，而在CCP中，纠缠熵以与z无关的最终质量尺度以明确的周期振荡，我们用相关器方法解释了这一现象。随着z的增大，纠缠熵增大，这可以用z引起的长程相互作用来理解。
We study the time evolution of the entanglement entropy after quantum quenches in Lifshitz free scalar theories, with the dynamical exponent z > 1, by using the correlator method. For quantum quenches we consider two types of time-dependent mass functions: end-critical-protocol (ECP) and cis-critical-protocol (CCP). In both cases, at early times the entanglement entropy is independent of the subsystem size. After a critical time (tc), the entanglement entropy starts depending on the subsystem size significantly. This critical time tc for z = 1 in the fast ECP and CCP has been explained well by the fast quasi-particle of the quasi-particle picture. However, we find that for z > 1 this explanation does not work and tc is delayed. We explain why tc is delayed for z > 1 based on the quasiparticle picture: in essence, it is due to the competition between the fast and slow quasiparticles. At late times, in the ECP, the entanglement entropy slowly increases while, in the CCP, it is oscillating with a well defined period by the final mass scale, independently of z. We give an interpretation of this phenomena by the correlator method. As z increases, the entanglement entropy increases, which can be understood by long-range interactions due to z.