论文标题
远程哈密顿人的时空淬火
Spatiotemporal Quenches in Long-Range Hamiltonians
论文作者
论文摘要
时空淬火在准备洛伦兹不变性的低能描述的关键哈密顿量的基态方面有效。具有最近邻居相互作用的临界横向场ISING模型，例如，用相对论低能量分散体的映射到自由费米子。然而，基于中性rydberg原子或被困离子的人工量子模拟器实现的自旋模型通常表现出与$ j（r）\ sim 1/r^α$相互作用的长距离幂律衰减，范围为$α$。在这项工作中，我们使用数值依赖于时间依赖的变分原理研究了这些模型中时空淬火的命运。对于$α\ gtrsim 3 $，建议具有动态关键指数$ z = 1 $的关键理论，我们的模拟表明，当前速度$ v $接近$ c $时，可以实现最佳冷却，这是关键模型中激发的有效速度。能量密度不均匀地分布在太空中，突出的热区域是由与淬火前部共同传播的激发堆积的，而通过反向传播激发填充的冷区域。降低$α$很大程度上模糊了这些区域之间的边界。对于$α<3 $，我们发现多普勒冷却效果消失了，如关键模型的重新归化组结果所预期的那样，这表明分散$ω\ sim q^z $，$ z <1 $。取而代之的是，我们表明激发由两个相关的长度尺度控制，它们的比例与前速度与阈值速度的比例有关，该速度最终决定了淬灭的绝热性。
Spatiotemporal quenches are efficient at preparing ground states of critical Hamiltonians that have emergent low-energy descriptions with Lorentz invariance. The critical transverse field Ising model with nearest neighbor interactions, for instance, maps to free fermions with a relativistic low energy dispersion. However, spin models realized in artificial quantum simulators based on neutral Rydberg atoms, or trapped ions, generically exhibit long range power-law decay of interactions with $J(r) \sim 1/r^α$ for a wide range of $α$. In this work, we study the fate of spatiotemporal quenches in these models with a fixed velocity $v$ for the propagation of the quench front, using the numerical time-dependent variational principle. For $α\gtrsim 3$, where the critical theory is suggested to have a dynamical critical exponent $z = 1$, our simulations show that optimal cooling is achieved when the front velocity $v$ approaches $c$, the effective speed of excitations in the critical model. The energy density is inhomogeneously distributed in space, with prominent hot regions populated by excitations co-propagating with the quench front, and cold regions populated by counter-propagating excitations. Lowering $α$ largely blurs the boundaries between these regions. For $α< 3$, we find that the Doppler cooling effect disappears, as expected from renormalization group results for the critical model which suggest a dispersion $ω\sim q^z$ with $z < 1$. Instead, we show that excitations are controlled by two relevant length scales whose ratio is related to that of the front velocity to a threshold velocity that ultimately determines the adiabaticity of the quench.
