Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
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DOI：
10.1103/physrevb.107.134202
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发表时间：
2022-11
影响因子：
3.7
通讯作者：
Stefano Piemontese;T. Roscilde;A. Hamma
中科院分区：
文献类型：
--
作者：
Stefano Piemontese;T. Roscilde;A. Hamma
在本文中，我们研究了一个典型的家庭状态的纠缠复杂性的转变-Rokhsar-Kivelson符号波函数-其纠缠度是由一个单一的参数控制。已知该状态族具有在呈现纠缠熵的体积律缩放的相位与具有纠缠的次扩展缩放的相位之间的转变，这让人想起无序量子哈密顿的多体局域化转变[Physical Review B 92，214204（2015）]。我们使用量子信息理论中的几种工具研究了Rokhsar-Kivelson符号波函数的奇异性及其在过渡过程中的纠缠复杂性：保真度度量;纠缠谱统计;纠缠熵波动;稳定剂R 'enyi熵;以及解纠缠算法的性能。在整个体积律阶段，态具有普遍的纠缠谱统计。然而，一个“超通用”的制度出现的控制参数的小值，其中所有的度量变得独立的参数本身;纠缠熵以及稳定剂R 'enyi熵似乎接近其理论最大值;纠缠波动规模为零，在随机通用电路的输出状态，和解纠缠算法基本上是零效率。所有这些指标一致揭示了一种复杂的纠缠模式。另一方面，在子体积律阶段，纠缠谱统计不再是普适的，纠缠波动更大，表现出非普适的标度;并且解纠缠算法的效率变得有限。我们的研究结果，基于模型波函数，表明纠缠标度特性和纠缠复杂性特征的类似组合可能会被发现在高能哈密顿本征态。
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 R\'enyi 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 R\'enyi 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.