论文标题
在本地量子系统中的有限温度上争夺信息
Information scrambling at finite temperature in local quantum systems
论文作者
论文摘要
本文调查了量子信息在具有能量差距（$ m $）的本地系统中的量子信息的温度依赖性。我们研究了由超级阶外相关器量化的海森堡运营商的速度和形状，特别注意所谓的轮廓依赖性，即对操作员在热圆周围分布的方式的依赖性。我们报告了一个与差距相当的温度下的大规模张量网络数字，这表明操作员的生长速度非常依赖于轮廓。该数字还显示了在有限温度$ t $下的操作员波前的特征扩展。为了研究低于差距的温度的行为，我们在2+1d O（$ n $）非线性Sigma模型的顺磁性阶段进行扰动计算，该模型在$ n $中是可以在分析上可触及的。使用梯形图技术，我们发现运算符在低温下以$ \ sqrt {t/m} $的速度传播，$ t \ ll m $。与自旋链的数值发现相反，大型$ n $计算对轮廓依赖性不敏感，并且没有显示对操作员前部的扩展。我们在最近提出的依赖国家依赖的情况下讨论了这些结果。
This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, $m$, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature $T$. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O($N$) non-linear sigma model, which is analytically tractable at large $N$. Using the ladder diagram technique, we find that operators spread at a speed $\sqrt{T/m}$ at low temperatures, $T\ll m$. In contrast to the numerical findings of spin chain, the large $N$ computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.
