Scrambling in the Dicke model

Abstract

The scrambling rate ${\lambda }_L$ associated with the exponential growth of out-of-time-ordered correlators can be used to characterize quantum chaos. Here we use the Majorana Fermion representation of spin $1/2$ systems to study quantum chaos in the Dicke model. We take the system to be in thermal equilibrium and compute ${\lambda }_L$ throughout the phase diagram to leading order in $1/N$. We find that the chaotic behavior is strongest close to the critical point. At high temperatures ${\lambda }_L$ is nonzero over an extended region that includes both the normal and super-radiant phases. At low temperatures ${\lambda }_L$ is nonzero in (a) close vicinity of the critical point and (b) a region within the super-radiant phase. In the process we also derive a new effective theory for the super-radiant phase at finite temperatures. Our formalism does not rely on the assumption of total spin conservation.

arXiv comment10 pages, 10 figures, 2 pages of appendix

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