论文标题
在具有强力法衰减相互作用的系统中，地面状态的局部性
Locality of gapped ground states in systems with power-law decaying interactions
论文作者
论文摘要
已经证明，在局部相互交互的量子系统的基差，局部扰动的影响随距离呈指数衰减。但是，在具有幂律的系统（$ 1/r^α$）腐烂的交互作用中，尚未显示出类似的陈述，并且存在严重的数学障碍来用现有方法证明这一点。在本文中，我们证明，当$α$超过空间尺寸$ d $时，本地扰动对本地属性的效果A距离$ r $ away的上限是由电源定律$ 1/r^{α_1} $处于宽大的地面状态，但前提是扰动不会缩小频谱间隙。如果$α> 2D $，并且交互是两体，那么$α_1$α_1$ $α_1$是紧密的，其中我们具有$α_1=α$。通过一种避免使用准绝热延续并结合复杂分析技术的方法可以实现证明。即使在短距离交互系统中，此方法也可以改善基态相关性衰减的界限。我们的工作概括了局部扰动对势力相互作用系统具有局部影响的基本观念，对数值模拟和实验具有广泛的影响。
It has been proved that in gapped ground states of locally-interacting quantum systems, the effect of local perturbations decays exponentially with distance. However, in systems with power-law ($1/r^α$) decaying interactions, no analogous statement has been shown, and there are serious mathematical obstacles to proving it with existing methods. In this paper we prove that when $α$ exceeds the spatial dimension $D$, the effect of local perturbations on local properties a distance $r$ away is upper bounded by a power law $1/r^{α_1}$ in gapped ground states, provided that the perturbations do not close the spectral gap. The power-law exponent $α_1$ is tight if $α>2D$ and interactions are two-body, where we have $α_1=α$. The proof is enabled by a method that avoids the use of quasiadiabatic continuation and incorporates techniques of complex analysis. This method also improves bounds on ground state correlation decay, even in short-range interacting systems. Our work generalizes the fundamental notion that local perturbations have local effects to power-law interacting systems, with broad implications for numerical simulations and experiments.
