论文标题
定时切片中免费费米子的纠缠熵
Entanglement Entropy of Free Fermions in Timelike Slices
论文作者
论文摘要
我们在一个离散点的任意时空切片中定义了自由fermion量子状态的纠缠熵，特别是研究了时代（因果）切片。对于具有能量带宽$ e_0 $的1D晶格免费费米子，我们计算了一组times $ t_n =nτ$（$ 1 \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le n \ le k $）的时间方向$ s_a $跨越同一站点上的时间长度$ t $。对于零温度接地状态，我们发现$ s_a $在$τ\ggτ_0=2π/e_0 $时显示量法。相反，$ s_a \ sim \ sim \ frac {1} {3} \ ln t $当$τ=τ_0$和$ s_a \ sim \ sim \ sim \ sim \ sim \ frac {1} {6} \ ln t $当$τ<τ_0$时，请与calabrese calabrese-cardy formal for n nonnonver chiral and Chiral and chiral and chiral and Chiral and Chiral and Chiral and Chiral and Chiral and Chiral and Chiral and Chiral and Chiral a。对于有限温度热状态，当$τ<τ_0$ $时，共同信息也会饱和。对于非元素，可以在$ s_a $中观察到$ t $的卷法和Lieb-Robinson绑定速度的签名。对于每个位置一个点的通用时空切片，零温度的纠缠熵显示，当切片从距离型到及时型不等时，从区域定律到体积定律的明确过渡。
We define the entanglement entropy of free fermion quantum states in an arbitrary spacetime slice of a discrete set of points, and particularly investigate timelike (causal) slices. For 1D lattice free fermions with an energy bandwidth $E_0$, we calculate the time-direction entanglement entropy $S_A$ in a time-direction slice of a set of times $t_n=nτ$ ($1\le n\le K$) spanning a time length $t$ on the same site. For zero temperature ground states, we find that $S_A$ shows volume law when $τ\ggτ_0=2π/E_0$; in contrast, $S_A\sim \frac{1}{3}\ln t$ when $τ=τ_0$, and $S_A\sim\frac{1}{6}\ln t$ when $τ<τ_0$, resembling the Calabrese-Cardy formula for one flavor of nonchiral and chiral fermion, respectively. For finite temperature thermal states, the mutual information also saturates when $τ<τ_0$. For non-eigenstates, volume law in $t$ and signatures of the Lieb-Robinson bound velocity can be observed in $S_A$. For generic spacetime slices with one point per site, the zero temperature entanglement entropy shows a clear transition from area law to volume law when the slice varies from spacelike to timelike.
