论文标题
纠缠熵和相空间密度：最低的Landau水平和1/2 BPS状态
Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
论文作者
论文摘要
我们考虑$ n $非权利主义费米子在$ 2+1 $ dimensions（LLL）级别的$ N $非权利性费米斯系统中的任意子区域的纠缠熵。利用这些状态与辅助$ 1+1 $尺寸的费米子系统的连接，我们根据相位空间密度运算符的期望值为$ 1+1 $尺寸，为领先的大$ n $贡献提供了一个表达式。对于适当的子区域，后者可以用其半经典的托马斯 - 弗米值代替，从而在明确的积分方面产生表达式，可以通过分析进行评估。我们表明，纠缠熵的主要术语是具有独立系数的外围定律。此外，我们获得了纠缠曲线上尖角的额外贡献的分析表达式。外围和角落均与特殊子区域的现有计算非常吻合。我们的结果与整数量子厅效应问题有关，以及$ \ Mathcal n = 4 $ yang Mills理论的半bps领域。在后一种情况下，我们认为的纠缠是目标空间中的纠缠。我们评论对衡量二元性的可能影响。
We consider the entanglement entropy of an arbitrary subregion in a system of $N$ non-relativistic fermions in $2+1$ dimensions in Lowest Landau Level (LLL) states. Using the connection of these states to those of an auxiliary $1+1$ dimensional fermionic system, we derive an expression for the leading large-$N$ contribution in terms of the expectation value of the phase space density operator in $1+1$ dimensions. For appropriate subregions the latter can replaced by its semiclassical Thomas-Fermi value, yielding expressions in terms of explicit integrals which can be evaluated analytically. We show that the leading term in the entanglement entropy is a perimeter law with a shape independent coefficient. Furthermore, we obtain analytic expressions for additional contributions from sharp corners on the entangling curve. Both the perimeter and the corner pieces are in good agreement with existing calculations for special subregions. Our results are relevant to the integer quantum Hall effect problem, and to the half-BPS sector of $\mathcal N=4$ Yang Mills theory on $S^3$. In this latter context, the entanglement we consider is an entanglement in target space. We comment on possible implications to gauge-gravity duality.
