Shannon and entanglement entropies of one- and two-dimensional critical wave functions
Shannon and entanglement entropies of one- and two-dimensional critical wave functions
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DOI：
10.1103/physrevb.80.184421
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发表时间：
2009-06
影响因子：
3.7
通讯作者：
Jean-Marie St'ephan;S. Furukawa;G. Misguich;V. Pasquier
中科院分区：
文献类型：
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作者：
Jean-Marie St'ephan;S. Furukawa;G. Misguich;V. Pasquier
研究了一维量子模型基态波函数概率分布的香农熵。该熵与由相应的二维经典模型建立的rokhsar - kivelson型波函数的纠缠熵有关。在临界和质量情况下，我们观察到它是由一个与系统长度成比例的广泛部分和一个次级普遍常数${S}_{0}$组成的。在$c=1$临界系统（Tomonaga-Luttinger液体）中，我们发现${S}_{0}$是玻色子紧化半径的简单函数。这一发现是基于对与二聚体和Calogero-Sutherland模型相关的Dyson-Gaudin气体的场理论分析。我们还对二聚体模型和自旋1/2 $XXZ$链进行了数值演示。在块状（晶体）相中，${S}_{0}$与基态简并有关。我们还研究了横向场中伊辛链中的熵，作为一个显示$c=1/2$临界点的例子。
We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant ${S}_{0}$. In $c=1$ critical systems (Tomonaga-Luttinger liquids), we find that ${S}_{0}$ is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 $XXZ$ chain. In a massive (crystal) phase, ${S}_{0}$ is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a $c=1/2$ critical point.