Ballistic propagation of a local impact in the one-dimensional XY model,Journal of Statistical Mechanics: Theory and Experiment

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Ballistic propagation of a local impact in the one-dimensional XY model
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.2 ) Pub Date : 2021-01-08 , DOI: 10.1088/1742-5468/abcd37
Atsuki Yoshinaga

We investigate propagation of a local impact in the one-dimensional $XY$ model with the anisotropy $\gamma$ in a magnetic field $h$. Applying a local and instantaneous unitary operation to the ground state, we numerically observe a light-cone-like propagation of the magnetization in the $z$ direction. In particular, we focus on the parameter region $0\leq\gamma\leq1$ and $0\leq h \leq2$ of the model. The dynamics in the light-cone region varies depending on the parameters. By combining numerical calculation with an asymptotic analysis, we find the following: (i) for $h\geq1-\gamma^{2}$ except for the case on the line $h=1$ with $0<\gamma<\sqrt{3}/2$, a wave front propagates with the maximum group velocity of quasiparticles, except for the case $\gamma=1$ and $0

中文翻译：

一维 XY 模型中局部撞击的弹道传播

我们研究了在磁场 $h$ 中具有各向异性 $\gamma$ 的一维 $XY$ 模型中局部影响的传播。将局部和瞬时幺正运算应用于基态，我们从数值上观察到磁化强度在 $z$ 方向上的光锥状传播。特别地，我们关注模型的参数区域 $0\leq\gamma\leq1$ 和 $0\leq h \leq2$。光锥区域的动力学因参数而异。通过将数值计算与渐近分析相结合，我们发现： (i) 对于 $h\geq1-\gamma^{2}$ 除了 $h=1$ 与 $0<\gamma<\sqrt {3}/2$，波前以准粒子的最大群速度传播，除了 $\gamma=1$ 和 $0 的情况

更新日期：2021-01-08

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