论文标题
多体定位过渡周围的本征态相关性
Eigenstate correlations around many-body localization transition
论文作者
论文摘要
我们探讨了本征态围绕多体定位（MBL）过渡的相关性，它们依赖于能量差（频率）$ω$和无序$ W $。除了真正的多体问题（随机场中的XXZ自旋链）外，我们还考虑在随机常规图（RRG）上定位，该图是MBL过渡的玩具模型。两种模型都表现出非常相似的行为。在过渡的局部侧，本征态相关函数$β（ω）$显示了与降低$ω$的相关性增强；相应的指数取决于$ W $。相邻的能量特征状态之间的相关性在过渡点$ w_c $处表现出最大值，可视化$ w_c $的漂移，而系统大小增加了其热力学限制值。相关函数$β（ω）$通过傅立叶变换与Hilbert-Space返回概率相关。我们讨论了最先进的量子计算机和模拟器上此类特征态相关函数的测量。
We explore correlations of eigenstates around the many-body localization (MBL) transition in their dependence on the energy difference (frequency) $ω$ and disorder $W$. In addition to the genuine many-body problem, XXZ spin chain in random field, we consider localization on random regular graphs (RRG) that serves as a toy model of the MBL transition. Both models show a very similar behavior. On the localized side of the transition, the eigenstate correlation function $β(ω)$ shows a power-law enhancement of correlations with lowering $ω$; the corresponding exponent depends on $W$. The correlation between adjacent-in-energy eigenstates exhibits a maximum at the transition point $W_c$, visualizing the drift of $W_c$ with increasing system size towards its thermodynamic-limit value. The correlation function $β(ω)$ is related, via Fourier transformation, to the Hilbert-space return probability. We discuss measurement of such (and related) eigenstate correlation functions on state-of-the-art quantum computers and simulators.
