Scrambling in the Dicke model

Abstract

The scrambling rate λL 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 λL 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 λL is nonzero over an extended region that includes both the normal and super-radiant phases. At low temperatures λL 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:1808.02038v2 [cond-mat.stat-mech]

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model

“…This work is supported by the Air Force Office of Scientific Research grants FA9550-18-1-0319 and its Multidisciplinary University Research Initiative grant(MURI), by the Defense Advanced Research Projects Agency (DARPA) and Army Research Office grant W911NF-16-1-0576, the National Science Foundation grant PHY-1820885, JILA-NSF grant PFC-173400, and the National Institute of Standards and Technology. Additional Note: Upon completion of this manuscript we became aware of the recent preprints [65,66], which present numerical and analytic investigation of OTOCs in the Dicke model. Author Contributions: The calculations were performed by R. L-S. and A. S-N. All authors participated in the conception of the project, analysis of the results and preparation of the manuscript.…”

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

“…It has been employed, for instance, in studies of ground-state and excited-state quantum phase tran-sitions [33,[40][41][42][43][44], entanglement creation [45], nonequilibrium dynamics [46][47][48][49], quantum chaos [50][51][52][53], and monodromy [54,55]. Recently, the model has received revived attention due to new experiments with ion traps [56,57] and the analysis of the OTOC [58,59].In the classical limit, the Dicke model presents regular and chaotic regions depending on the Hamiltonian parameters and excitation energies [53]. This allows us to benchmark the OTOC growth against the presence and absence of chaos.…”

Out-of-time-order correlations and Floquet dynamical quantum phase transition

“…Recently, out-of-time-order correlation (OTOC) has gained much attention in the physics community across many different fields, due to its feasibility in experiments [1][2][3][4][5][6][7][8] and also its richness in theoretical physics [9][10][11][12][13][14][14][15][16][17][18][19][20][21][22][23][24][25]. Recent progress in the experimental detection of quantum correlations and in quantum control techniques applied to systems as photons, molecules, and atoms, made it possible to direct observation of an OTOC in nuclear magnetic resonance quantum simulator [6,8] and trapped ions quantum magnets [5].…”

“…Lately, it has been revitalized, because it propounds an interesting and different insight into physical systems [23]. Some of the most important results involve the dynamics of quantum systems [9][10][11][12][13][14] such as quantum information scrambling [14][15][16][17][18][19][20][21][22] and quantum entanglement [15,24]. The decay of OTOC is closely related to the delocalization of information and implies the information-theoretic definition of scrambling.…”