Temporal fluctuations of correlators in integrable and chaotic quantum systems
Temporal fluctuations of correlators in integrable and chaotic quantum systems
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DOI：
10.21468/scipostphys.15.6.244
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发表时间：
2023-07
期刊：
影响因子：
5.5
通讯作者：
Talía L. M. Lezama;Yevgeny Bar Lev;L. F. Santos
中科院分区：
文献类型：
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作者：
Talía L. M. Lezama;Yevgeny Bar Lev;L. F. Santos
我们在无能隙简并的多体量子系统的超时有序和时间有序相关器的无限时间平均值附近提供了时间涨落的界限。对于物理初始态，我们的边界预测了时间涨落作为系统大小的函数的指数衰减。我们对满足我们假设的混沌和相互作用的自旋1/2可积链进行了数值验证。另一方面，我们从解析和数值上证明了对于XX模型这一具有能隙简并的非相互作用系统，对于费米子表象中的局域算符，时间涨落随系统大小呈多项式衰减，而对于非局域算符，时间涨落随系统大小呈指数衰减。我们的结果表明，相关器的长时间时间涨落的衰变不能作为混沌或缺乏混沌的可靠度量。
We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size. We numerically verify this prediction for chaotic and interacting integrable spin-1/2 chains, which satisfy the assumption of our bounds. On the other hand, we show analytically and numerically that for the XX model, which is a noninteracting system with gap degeneracies, the temporal fluctuations decay polynomially with system size for operators that are local in the fermion representation and decrease exponentially in the system size for non-local operators. Our results demonstrate that the decay of the long-time temporal fluctuations of correlators cannot be used as a reliable metric of chaos or lack thereof.