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arXiv 2007.06989quant-phcond-mat.dis-nncond-mat.stat-mech
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量子自旋链中的涌现纠缠结构和自相似性

Emergent entanglement structures and self-similarity in quantum spin chains

Boris Sokolov, Matteo A. C. Rossi, Guillermo García-Pérez, Sabrina Maniscalco

摘要:

基于多体量子态中各组分之间的纠缠,提出了一种实验上可实现的多体量子态网络表示。我们通过将其应用于一个典型的自旋链模型,XX模型,并表明它带来了新的现象,说明了这种表示的力量。这些纠缠网络的分析表明,准长程序的逐步建立伴随着单自旋并发分布的对称性,以及网络拓扑结构的不稳定性。此外,我们确定了紧急纠缠结构的存在,空间本地化的社区强制执行的系统的全球对称性,可以通过模型不可知的社区检测算法。网络表示进一步揭示了存在的结构类和循环自相似的状态,我们推测是密切相关的社区结构。我们的研究结果表明,使用复杂网络理论的工具和概念,即使在研究了几十年的模型中,也可以发现,理解和描述新的物理现象。

英文摘要:

We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localised communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding, and description of new physical phenomena even in models studied for decades.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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