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 $α^* < 1$.
Imaginary Time Spectral Transforms for Excited State Preparation
IBM Quantum, IBM Research Europe（IBM量子，IBM欧洲研究院）；University of Southampton（南安普顿大学）；The Hartree Centre, STFC（哈特里中心，STFC）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；SUPA, School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院，SUPA）
Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
Huse { \it et al} [Phys. Rev. B { \bf 88}，014206（2013）]和Elisran { \it et al} [Phys. Rev. B 89，144201（2014）]提出了一种反直觉的预期：即使在高激发本征态中，局域化也保护基态的量子顺序。在这项工作中，我们数值研究的本地化保护的拓扑（SPT）秩序考虑修改后的XXZ自旋模型，相关的相互作用的Su-Schrieffer-Heeger（SSH）模型。我们系统地研究了多体局域化（MBL）如何保护SPT对不同类型的疾病和不同形式的相互作用。一定的无序度导致各激发多体本征态的低纠缠谱明显简并。这一事实表明，存在的边缘模式，这是一个标志的SPT秩序，是由MBL在激发多体本征态的保护。此外，我们还报告了如何MBL保护边缘模式在激发多体本征态消失的对角型无序。
