论文标题
典型链中的非本地自旋纠缠
Non-local spin entanglement in a fermionic chain
论文作者
论文摘要
有效的两旋密度矩阵（TSDM），用于一对旋转$ 1/2 $的自由度，居住在稀疏的费米海中的$ r $，可以从在物理中规定的框架后从两电子密度矩阵中获得。 Rev. A 69，054305（2004）。我们注意到，从该TSDM获得的单个自旋密度矩阵（SSDM），用于仿制的自旋定性系统的自由费用系统总是固定在最大混合状态$的$ $ $ $（1/2）\ \ \ \ \ \ \ \ \ mathbb {i} $中，与距离$ r $无关，而tsdm则与Maximsect of Maxim fin ot for n ot for n ost for n ost for n ost for n ost in n ost in n ost in n ost ot ot ot Maximed ot ot fine' $ r $。 X状态在$ r \ rightArrow 0 $限制中降低到纯状态（单圈），而它饱和到X-state，von-Neumann熵的最大允许价值为$ 2 \ ln2 $，为$ r \ rightarrow \ rightarrow \ rightarrow \ infty \ infty $，独立于化学潜力的价值。但是，一旦应用了外部磁场来提高自旋排行证，我们发现SSDM的von-Neumann熵成为两个旋转之间距离$ r $的函数。我们还表明，$ r \ rightarrow \ infty $限制中TSDM的von-Neumann熵成为化学势的函数，并且仅当频段完全填充的频段与自旋脱位外壳不同时，它才饱和至$ 2 \ ln2 $。最后，我们将研究扩展到包括自旋轨道耦合，并表明它确实会影响这些渐近结果。我们的发现与以前的作品形成鲜明对比，这些作品是基于晶格模型的物理学的连续模型。
An effective two-spin density matrix (TSDM) for a pair of spin-$1/2$ degree of freedom, residing at a distance of $R$ in a spinful Fermi sea, can be obtained from the two-electron density matrix following the framework prescribed in Phys. Rev. A 69, 054305 (2004). We note that the single spin density matrix (SSDM) obtained from this TSDM for generic spin-degenerate systems of free fermions is always pinned to the maximally mixed state $i.e.$ $(1/2) \ \mathbb{I}$, independent of the distance $R$ while the TSDM confirms to the form for the set of maximally entangled mixed state (the so called "X-state") at finite $R$. The X-state reduces to a pure state (a singlet) in the $R\rightarrow 0$ limit while it saturates to an X-state with largest allowed value of von-Neumann entropy of $2 \ln2$ as $R \rightarrow \infty$ independent of the value of chemical potential. However, once an external magnetic field is applied to lift the spin-degeneracy, we find that the von-Neumann entropy of SSDM becomes a function of the distance $R$ between the two spins. We also show that the von-Neumann entropy of TSDM in the $R\rightarrow \infty$ limit becomes a function of the chemical potential and it saturate to $2 \ln2$ only when the band in completely filled unlike the spin-degenerate case. Finally we extend our study to include spin-orbit coupling and show that it does effect these asymptotic results. Our findings are in sharp contrast with previous works which were based on continuum models owing to physics which stem from the lattice model.
