论文标题
具有随机长距离相互作用的XX旋转链的激发 - 纤维素态纠缠特性
Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions
论文作者
论文摘要
量子信息理论措施是表征量子动态阶段的有用工具。但是，雇用它们来研究随机旋转系统的激发状态是一个具有挑战性的问题。在这里，我们报告了随机XX抗铁磁链链的纠缠熵（EE）尺度的结果，具有长距离（LR）相互作用的衰减，这是具有距离的功率定律，且指数$α$。为此，我们扩展了激发态（RSRG-X）的真实空间重归其化组技术，以解决LR相互作用的问题。为了进行比较，我们执行数值精确的对角（ED）计算。从ED最多可为$ n \ sim 18 $旋转的能量水平间距的分布中，我们发现在能量谱的中间，在$α_c\ \ 1 $处的定位过渡的迹象。 With RSRG-X and ED, we show that for $α>α^*$ the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $α<α^*$ EE displays an algebraic growth with the subsystem size $l$, $S_l\sim l^β$, with $ 0 <β<1 $。我们发现$α^* \大约1 $与多体频谱中间的DELACALIZER TRUNCETION $α_C$重合。提出了基于RG规则的结构对这些结果的解释，这是由于非常长距离相互作用$α\ ll 1 $引起的{\ it Rainbow}增殖。我们还研究了EE的有效温度依赖性，使我们能够在不同能量密度下研究本征态的半链纠缠熵，我们发现EE中的交叉发生在$α^* <1 $。
Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $α$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of a delocalization transition at $α_c \approx 1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $α>α^*$ the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $α<α^*$ EE displays an algebraic growth with the subsystem size $l$, $S_l\sim l^β$, with $0<β<1$. We find that $α^* \approx 1$ coincides with the delocalization transition $α_c$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to {\it rainbow} proliferation for very long-range interactions $α\ll 1$. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at $α^* < 1$.
