论文标题
具有半序的初始状态的假想时间量子松弛临界动力学
Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States
论文作者
论文摘要
我们探索具有半排序初始状态的量子临界点附近的假想时间松弛动力学。与均质有序初始状态的情况不同，在该状态下，$ m $均匀衰减为$ m \ proptoτ^{ - β/νz} $，此处$ m $取决于位置$ x $，显示出丰富的缩放行为。类似于模型A中具有初始域壁的经典弛豫动力学，该动力学描述了纯粹的耗散动力学，随着虚构时间的发展，域壁扩展到界面区域，大小不断增长。在界面区域中，本地顺序参数为$ m \ proptoτ^{ - β_1/νz} $，$β_1$是一个附加的动态关键指数。远离界面区域的局部顺序参数在短时间阶段呈$ m \ proptoτ^{ - β/νz} $，然后跨越$ m \ proptoτ^{ - β_1/νz} $的缩放行为。开发了表征这些缩放特性的完整缩放形式。以一个维度和二维中的量子模型作为验证缩放理论的示例。此外，我们发现对于量子模型，缩放函数是一个分析函数，$β_1$不是独立的指数。
We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial states, in which the order parameter $M$ decays homogeneously as $M\propto τ^{-β/νz}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical relaxation dynamics with an initial domain wall in Model A, which describes the purely dissipative dynamics, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto τ^{-β_1/νz}$, with $β_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto τ^{-β/νz}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto τ^{-β_1/νz}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $β_1$ is not an independent exponent.
