arXiv 1201.63672012-01hep-thcond-mat.stat-mechcond-mat.str-el

关联长度与纠缠熵的反常修正

Correlation Length and Unusual Corrections to the Entanglement Entropy

Elisa Ercolessi, Stefano Evangelisti, Fabio Franchini, Francesco Ravanini

备注：: 11 pages, 4 figures; Updated published version, with revised introduction
发表信息：: Phys. Rev. B 85, 115428 (2012)
DOI：: 10.1103/PhysRevB.85.115428

摘要：

我们研究分析的修正的主要条款在Renyi熵的大规模晶格理论，表现出显着的偏离天真的期望。特别是，我们表明，有限的大小和有限的质量效应引起不同的贡献（不同的指数），从而违反了一个简单的缩放参数。在具体的，我们看的纠缠熵的两体XYZ自旋1/2链在其基态。当系统被分成两个半无限半链时，我们得到了Renyi熵作为单个质量参数的函数的解析表达式。在标度极限下，我们证明了熵作为关联长度的函数形式上与体伊辛模型一致。这应该是比较的事实，在临界状态下，该模型是由一个c=1共形场论和修正熵由于有限尺寸效应显示指数依赖于理论的紧化半径。我们将论证这些陈述之间并不矛盾。如果晶格间距是有限的，质量参数和相关长度之间的关系产生新的次主导项的熵，其形式是路径依赖的相空间和场论内的解释还没有。这些贡献是由于稳定束缚态的存在而产生的，因此是真正相互作用理论（如XYZ链）的一个独特特征。

英文摘要：

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Renyi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 Conformal Field Theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path-dependent in phase-space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain.

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