论文标题
一维$ xy $型号中局部影响的弹道传播
Ballistic propagation of a local impact in the one-dimensional $XY$ model
论文作者
论文摘要
信息的灯光般的传播是可整合自旋系统非平衡动力学的普遍现象。在本文中，我们通过计算磁化材料来调查一维$ XY $模型中局部影响的传播，该模型在磁场$ h $中通过计算磁化材料来调查磁场$γ$。我们将本地和瞬时的统一操作应用于基态，我们称为本地影响协议，我们从数值上观察了该模型的参数区域中的各种类型的轻孔状传播$ 0 \leqγ\ leq \ leq leq1 $和$ 0 \ leq h \ leq h \ leq h \ leq2 $。通过将数值集成与渐近分析相结合，我们找到以下内容：（i）对于$ | h | \ geq |1-γ^{2} | $，除了$ h = 1 $的情况外，$ 0 <γ<γ<\ sqrt {3}/2 $，the proft tave proft ciste $ and quasipiptiles，for quasipipticles，for quasipiptiles，for quasipipity， $ 0 <h <1 $，其中没有清晰的波阵； （ii）对于$ | h | <| <|1-γ^{2} | $，以及在线$ h = 1 $，带有$ 0 <γ<\ sqrt {3}/2 $，第二波阵前是由于组速度的多个局部极端出现的， （iii）对于$ | h | = | = |1-γ^{2} | $，第二波前部的边缘在原点倒塌，因此，磁化曲线在受影响的位点显示了山脊。此外，我们通过一个渐近分析发现，波浪阵线的高度在时间$ t $中衰减各种指数，具体取决于模型参数：波阵面展示了一个幂律衰减$ t^{ - 2/3} $，除非$ h = 1 $，nine $ h = 1 $，可以通过$ \ sim the $ \ sim t^$ \ sim t^$ 3/3/5} { - 3/3/3/5/3/5/5/5}。 t^{ - 1} $; $ | h | = |1-γ^{2} | $在受影响地点的山脊显示衰减$ t^{ - 1/2} $，而其他情况则与衰减$ t^{ - 1} $相反。
Light-cone-like propagation of information is a universal phenomenon of nonequilibrium dynamics of integrable spin systems. In this paper, we investigate propagation of a local impact in the one-dimensional $XY$ model with the anisotropy $γ$ in a magnetic field $h$ by calculating the magnetization profile. Applying a local and instantaneous unitary operation to the ground state, which we refer to as the local-impact protocol, we numerically observe various types of light-cone-like propagation in the parameter region $0\leqγ\leq1$ and $0\leq h \leq2$ of the model. By combining numerical integration with an asymptotic analysis, we find the following: (i) for $|h|\geq|1-γ^{2}|$ except for the case on the line $h=1$ with $0<γ<\sqrt{3}/2$, a wave front propagates with the maximum group velocity of quasiparticles, except for the case $γ=1$ and $0<h<1$, in which there is no clear wave front; (ii) for $|h|<|1-γ^{2}|$ as well as on the line $h=1$ with $0<γ<\sqrt{3}/2$, a second wave front appears owing to multiple local extrema of the group velocity; (iii) for $|h|=|1-γ^{2}|$, edges of the second wave front collapses at the origin, and as a result, the magnetization profile exhibits a ridge at the impacted site. Furthermore, we find by an asymptotic analysis that the height of the wave front decays in a power law in time $t$ with various exponents depending on the model parameters: the wave fronts exhibit a power-law decay $t^{-2/3}$ except for the line $h=1$, on which the decay can be given by either $\sim t^{-3/5}$ or $\sim t^{-1}$; the ridge at the impacted site for $|h|=|1-γ^{2}|$ shows the decay $t^{-1/2}$ as opposed to the decay $t^{-1}$ in other cases.
