论文标题
Lieb Robinson在远程自旋链中的界限和超出时间顺序相关器
Lieb Robinson bounds and out of time order correlators in a long range spin chain
论文作者
论文摘要
Lieb Robinson界限量化了非顾问量子系统中信息传播的最大速度。我们讨论了Lieb Robinson与超时订单相关器的关系，这与换向器的不同规范$ c（r，t）= [a_i（t），b_i（t），b_ {i+r}]本地运营商的$。使用精确的Krylov时空演变技术，我们计算了Spin 1/2 Heisenberg链的这两个不同规范，其交互作用衰减为Power Law $ 1/r^α$，并带有距离$ r $。我们的数值分析表明，两种规范（操作员规范和标准化的Frobenius Norm）都表现出相同的渐近行为，即短时间内的线性增长和长距离空间的功率定律衰减，从而使Power Law Laws Light Light Cones以$ $α<1 $ $ <1 $和线性光锥的线性光锥（$α> 1 $）。 $ c（r，t）\ propto t/r^α$的尾巴的渐近形式是用短时扰动理论描述的，该理论在短时间内有效。
Lieb Robinson bounds quantify the maximal speed of information spreading in nonrelativistic quantum systems. We discuss the relation of Lieb Robinson bounds to out of time order correlators, which correspond to different norms of commutators $C(r,t) = [A_i(t),B_{i+r}]$ of local operators. Using an exact Krylov space time evolution technique, we calculate these two different norms of such commutators for the spin 1/2 Heisenberg chain with interactions decaying as a power law $1/r^α$ with distance $r$. Our numerical analysis shows that both norms (operator norm and normalized Frobenius norm) exhibit the same asymptotic behavior, namely a linear growth in time at short times and a power law decay in space at long distance, leading asymptotically to power law light cones for $α<1$ and to linear light cones for $α>1$. The asymptotic form of the tails of $C(r,t)\propto t/r^α$ is described by short time perturbation theory which is valid at short times and long distances.
