arXiv 1408.06372014-08hep-thcond-mat.str-elquant-ph

激发态不相交区域的纠缠熵：算符方法

Entanglement Entropy of Disjoint Regions in Excited States : An Operator Method

Noburo Shiba

备注：: 22 pages; v3, typos corrected, published version
发表信息：: JHEP12(2014)152
DOI：: 10.1007/JHEP12(2014)152

摘要：

基于将子系统$Ω$的密度矩阵表示为$Trρ_Ω^n$，并将其表示为局域算符的期望值的思想，发展了纠缠熵的计算方法.我们应用它来考虑不相交的紧凑空间区域$A$和$B$的相互Renyi信息$I^{(n)}(A,B)=S^{(n)}_A+S^{(n)}_B-S^{(n)}_{A\cup B}$的局部激发态定义的本地运营商在$A$和$B$上的$(d+1)$维场论的真空，在极限时，$A$和$B$之间的分离$r$远大于它们的大小$R_{A,B}$。对于具有质量间隙的一般量子场论，我们计算了$I^{(n)}(A,B)$，发现这个结果可以用量子力学中的纠缠态来解释。对于自由无质量标量场，我们证明了对于某些激发态，$I^{(n)}(A,B)-I^{(n)}(A,B)|_{r \rightarrow \infty} =C^{(n)}_{AB}/r^{α(d-1)}$，其中$α=1$或2由局域算符在真空态的变换$ϕ\rightarrow -ϕ$和$α=2$下的性质决定.给出了系统地计算$C^{(2)}_{AB}$的方法。

英文摘要：

We develop the computational method of entanglement entropy based on the idea that $Trρ_Ω^n$ is written as the expectation value of the local operator, where $ρ_Ω$ is a density matrix of the subsystem $Ω$. We apply it to consider the mutual Renyi information $I^{(n)}(A,B)=S^{(n)}_A+S^{(n)}_B-S^{(n)}_{A\cup B}$ of disjoint compact spatial regions $A$ and $B$ in the locally excited states defined by acting the local operators at $A$ and $B$ on the vacuum of a $(d+1)$-dimensional field theory, in the limit when the separation $r$ between $A$ and $B$ is much greater than their sizes $R_{A,B}$. For the general QFT which has a mass gap, we compute $I^{(n)}(A,B)$ explicitly and find that this result is interpreted in terms of an entangled state in quantum mechanics. For a free massless scalar field, we show that for some classes of excited states, $I^{(n)}(A,B)-I^{(n)}(A,B)|_{r \rightarrow \infty} =C^{(n)}_{AB}/r^{α(d-1)}$ where $α=1$ or 2 which is determined by the property of the local operators under the transformation $ϕ\rightarrow -ϕ$ and $α=2$ for the vacuum state. We give a method to compute $C^{(2)}_{AB}$ systematically.

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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