论文标题
非相互作用的费米子系统中的数字熵在纠缠熵上的边界
Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems
论文作者
论文摘要
多体系统的纯净状态的纠缠可以以rényi熵为特征，$ s^{（α）} = \ ln \ textrm {tr}（ρ^α）/（1-α）/（1-α）$的降低密度矩阵$ρ$的子系统。但是，这些熵很难在实验上访问，通常只能针对小型系统确定。在这里，我们表明，对于以高斯状态和粒子数保护的自由效费系统，$ \ ln s^{（2）} $可以受到更容易访问的rényinumber entropy $ s^{（2）} _ n = - \ \ sum_n \ sum_n p^2（n）$ sublosive y Intermity $ submity $ p（n）的函数$ p（n）的函数$ p（n）的函数（$ p（n）的函数（$）$ p（$因此，尤其是纠缠的动态增长总是伴随着数量熵的对数较慢的生长。我们通过在非相互作用的一维晶格模型（包括无障碍，安德森 - 位置化和患有异性疾病的关键系统）中呈现淬灭的淬火结果来说明这种关系。
Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies $S^{(α)}=\ln\textrm{tr}(ρ^α)/(1-α)$ of the reduced density matrix $ρ$ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, $\ln S^{(2)}$ can be tightly bound by the much easier accessible Rényi number entropy $S^{(2)}_N=-\ln \sum_n p^2(n)$ which is a function of the probability distribution $p(n)$ of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth---albeit logarithmically slower---of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal disorder.
