Bound on the exponential growth rate of out-of-time-ordered correlators.
Bound on the exponential growth rate of out-of-time-ordered correlators.
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DOI：
10.1103/physreve.98.012216
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
N. Tsuji;Tomohiro Shitara;Masahito Ueda
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文献类型：
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作者：
N. Tsuji;Tomohiro Shitara;Masahito Ueda
这是由Maldacena， Shenker和Stanford推测出来的[J]。Maldacena， S. H. Shenker, and D. Stanford， J. High Energy physics . 08(2016) 10610.1007/JHEP08(2016)106]证明了超时序相关器（OTOC） F(t)的指数增长率有一个普适上界2πk_{B} t / h。本文引入了一组单参数的非时序相关器F_{γ}(t)(0≤γ≤1)，它具有与F(t)一样好的性质，是对非时序部分的平方换易子< [a [/ n](t),B[/ n](0)]^{2} >的正则化，可以诊断量子多体混沌，并且在γ=1/2处与F(t)重合。我们严格证明了如果F_{γ}(t)在0≤γ≤1范围内对所有γ都呈瞬态指数增长，即无论选择何种正则化，OTOC都呈指数增长，则增长率λ不依赖于正则化参数γ，且满足不等式λ≤2πk_{B} t / h。
It has been conjectured by Maldacena, Shenker, and Stanford [J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 10610.1007/JHEP08(2016)106] that the exponential growth rate of the out-of-time-ordered correlator (OTOC) F(t) has a universal upper bound 2πk_{B}T/ℏ. Here we introduce a one-parameter family of out-of-time-ordered correlators F_{γ}(t) (0≤γ≤1), which has as good properties as F(t) as a regularization of the out-of-time-ordered part of the squared commutator 〈[A[over ̂](t),B[over ̂](0)]^{2}〉 that diagnoses quantum many-body chaos, and coincides with F(t) at γ=1/2. We rigorously prove that if F_{γ}(t) shows a transient exponential growth for all γ in 0≤γ≤1, that is, if the OTOC shows an exponential growth regardless of the choice of the regularization, then the growth rate λ does not depend on the regularization parameter γ and satisfies the inequality λ≤2πk_{B}T/ℏ.