论文标题
rokhsar-kivelson-sign波形的纠缠复杂性
Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
论文作者
论文摘要
在本文中，我们研究了一个典型的状态家族中纠缠复杂性的转变 - rokhsar -kivelson -sign波函数 - 其纠缠程度由单个参数控制。已知这个国家的家族具有表现出纠缠熵的相位体积尺度的相位和具有范围内尺度缩放的相位，使人联想到无序量子汉密尔顿的多体定位过渡[物理评论B 92，214204（2015）]。我们使用量子信息理论中的多种工具：保真度度量，研究了Rokhsar-Kivelson-Sign波函数的奇异性及其在整个过渡过程中的纠缠复杂性；纠缠频谱统计；纠缠熵波动；稳定器Rényi熵；以及分解算法的性能。在整个体积阶段，状态具有通用纠缠频谱统计。然而，对于控制参数的小值而言，出现了“超级大学”制度，其中所有指标都独立于参数本身。纠缠熵以及稳定器rényi熵似乎接近其理论上的最大值。随机通用电路的输出状态和解开算法的纠缠波动量表降至零，基本上具有无效的效率。所有这些指标始终揭示出复杂的纠缠模式。另一方面，在子批量法阶段中，纠缠频谱统计不再普遍，纠缠波动较大，并且表现出非宇宙缩放。并且分解算法的效率成为有限的。我们的结果基于模型波函数，表明在高能量的哈密顿特征态中可以发现纠缠缩放特性和纠缠复杂性特征的类似组合。
In this paper we study the transitions of entanglement complexity in an exemplary family of states - the Rokhsar-Kivelson-sign wavefunctions - whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with sub-extensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians [Physical Review B 92, 214204 (2015)]. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric; entanglement spectrum statistics; entanglement entropy fluctuations; stabilizer Rényi Entropy; and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a "super-universal" regime appears for small values of the control parameter in which all metrics become independent of the parameter itself; the entanglement entropy as well as the stabilizer Rényi entropy appear to approach their theoretical maximum; the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a non-universal scaling; and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates.
