二维旋转费米子激发态中的纠缠标度与全计数统计
Entanglement Scaling and Full Counting Statistics in Excited States of Two-Dimensional Rotating Fermions
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中文总结 AI 辅助
本文研究二维旋转费米子激发态的纠缠标度与全计数统计，验证激发态纠缠熵满足面积定律，推导环形区域相关量的加性关系，拓展了非相互作用费米子的纠缠性质研究。
中文摘要 AI 辅助
我们研究了被限制在二维简谐势阱中、以角频率Ω旋转的一类N粒子费米子激发态的纠缠熵。该激发态通过填充一组特定的N个单粒子能级构建而成。我们解析计算了势阱中心周围半径为r的圆盘内q阶Rényi熵，以及该圆盘内费米子数涨落对应的累积量。研究发现，即使对于这类激发态，纠缠熵的面积定律标度依然成立。我们还验证了非相互作用费米子的纠缠熵关于粒子数累积量的著名级数展开。我们进一步推导了中心累积量生成函数，证明该圆盘内的关联概率分布函数在可变平移下，与已知的基态结果具有相同的标度性质。最后，我们将结果推广到环形区域，表明环形区域的Rényi熵和粒子数累积量可分解为其两个边界圆盘对应量的和，只要环形区域的宽度足够大，这些加性关系就成立。
英文摘要
We investigate the entanglement entropy of a class of $N$-particle excited state of fermions confined in a two-dimensional harmonic trap rotating at an angular frequency $Ω$. The excited state is constructed by filling a particular set of $N$ single-particle energy levels. We analytically compute the Rényi entropies of order $q$ in a disc of radius $r$ around the centre of the trap, and the cumulants corresponding to number fluctuations of fermions within the disc. We found that the area law scaling of entanglement entropy holds even for a class of excited states. We also verified the well-known series expansion of entanglement entropy in terms of the particle number cumulants for non-interacting fermions. We further derive the centered cumulant generating function, demonstrating that the associated probability distribution function in the disc has identical scaling properties, up to a variable shift, to the known ground-state result. Finally, we extend our result to an annular region, showing that both the Rényi entropy and particle number cumulants of the annulus decompose into sums of the corresponding quantities of the two bounding discs. These additive relations hold as long as the width of the annulus is sufficiently large.
