论文标题
自由schrödinger场理论中间隔的纠缠熵在有限密度
Entanglement entropies of an interval in the free Schrödinger field theory at finite density
论文作者
论文摘要
我们研究了有限密度和零温度下的自由式无旋转schrödinger场理论中无限线上间隔的纠缠熵，这是一个非相关模型，其中lifshitz指数$ z = 2 $。我们证明，纠缠熵是一个无量纲参数的有限函数，与由费米动量和间隔的长度确定的相空间中的矩形区域成正比。纠缠熵是单调增加的功能。通过采用零阶的岩体球形波的特性或正弦核的tau功能的渐近膨胀，我们发现了纠缠熵在相位空间中矩形大面积和大面积区域的渐近方向上的扩展的分析表达式。这些扩展导致证明相对论熵$ c $函数的类似物不是单调的。将我们的分析扩展到由其整数动态指数$ z $标记的一类免费的费米子Lifshitz模型，我们发现该指数的奇偶校验决定了两条间隔的两分纠缠的属性。
We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrödinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent $z=2$. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic $C$ function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent $z$, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.
