具有幂律衰减相互作用的自旋模型中的多速预热化
Multi-speed prethermalization in spin models with power-law decaying interactions
摘要：
具有有限程相互作用的均匀量子系统在猝灭后的弛豫一般由足够小的猝灭触发的长寿命准粒子激发的弹道传播驱动。在这里，我们调查的情况下，（$1/r^α$）的相互作用的$d$维晶格自旋模型与单轴对称，并表明，在政权$d < α< d+2$，纠缠和相关建设是从根本上改变了准粒子，$ω\sim k^{z<1}$，在小波矢量的非线性色散关系的存在，导致准粒子群速度和超弹道传播的发散。当聚焦于$k=0$波动时，这转化为相关前沿随时间的超线性增长，以及子系统可观测量的弛豫时间随大小的次线性增长。然而，群速度的大色散导致有限$k$波动的弛豫时间的极端波长依赖性，其中最长的波动对纠缠敏感。我们的预测是直接相关的，目前的实验探测囚禁离子，或超冷磁性和里德伯原子在光晶格的非平衡动力学。
英文摘要：
The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasi-particle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range ($1/r^α$) interactions for $d$-dimensional lattice spin models with uniaxial symmetry, and show that, in the regime $d < α< d+2$, the entanglement and correlation buildup is radically altered by the existence of a non-linear dispersion relation of quasi-particles, $ω\sim k^{z<1}$, at small wave vectors, leading to a divergence of the quasiparticle group velocity and super-ballistic propagation. This translates in a super-linear growth of correlation fronts with time, and sub-linear growth of relaxation times of subsystem observables with size, when focusing on $k=0$ fluctuations. Yet the large dispersion in group velocities leads to an extreme wavelength dependence of relaxation times of finite-$k$ fluctuations, with entanglement being susceptible to the longest of them. Our predictions are directly relevant to current experiments probing the nonequilibrium dynamics of trapped ions, or ultracold magnetic and Rydberg atoms in optical lattices.
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